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Journal articles on the topic 'Notion of derivative'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Valiukevičius, G. "Notion of the virtual derivative." Nonlinear Analysis: Modelling and Control 16, no. 1 (January 25, 2011): 116–22. http://dx.doi.org/10.15388/na.16.1.14119.

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Formal graphical procedures to calculate function’s derivative are proposed. This can be applied to calculate expressions of geometric objects, construct approximate schemes in numerical analysis of solution of differential equation.

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2

Lango, John W. "Whitehead’s Derivative Notion of Societies." Process Studies 36, no. 1 (2007): 89–107. http://dx.doi.org/10.5840/process200736123.

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3

Brualdi, Richard A., and Geir Dahl. "Permutation Matrices, Their Discrete Derivatives and Extremal Properties." Vietnam Journal of Mathematics 48, no. 4 (March 24, 2020): 719–40. http://dx.doi.org/10.1007/s10013-020-00392-5.

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AbstractFor a permutation π, and the corresponding permutation matrix, we introduce the notion of discrete derivative, obtained by taking differences of successive entries in π. We characterize the possible derivatives of permutations, and consider questions for permutations with certain properties satisfied by the derivative. For instance, we consider permutations with distinct derivatives, and the relationship to so-called Costas arrays.

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4

Feng, Xiaobing, and Mitchell Sutton. "A new theory of fractional differential calculus." Analysis and Applications 19, no. 04 (February 20, 2021): 715–50. http://dx.doi.org/10.1142/s0219530521500019.

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This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer order weak derivatives; it also helps to unify multiple existing fractional derivative definitions and characterize what functions are fractionally differentiable. Various calculus rules including a fundamental theorem calculus, product and chain rules, and integration by parts formulas are established for weak fractional derivatives. Additionally, relationships with classical fractional derivatives and detailed characterizations of weakly fractional differentiable functions are also established. Furthermore, the notion of weak fractional derivatives is also systematically extended to general distributions instead of only to some special distributions. This new theory lays down a solid theoretical foundation for systematically and rigorously developing new theories of fractional Sobolev spaces, fractional calculus of variations, and fractional PDEs as well as their numerical solutions in subsequent works.

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5

Norfield, Tony. "Derivatives, Money, Finance and Imperialism: A Response to Bryan and Rafferty." Historical Materialism 21, no. 2 (2013): 149–68. http://dx.doi.org/10.1163/1569206x-12341296.

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Abstract This paper contributes to the debate on the role of financial derivatives for capitalism. It responds to Bryan and Rafferty’s defence of their analysis and their critique of my own. The paper argues that their analysis confuses what a financial derivative does, and mixes together different kinds of derivative – and non-derivative – that play very different roles. After detailing these points, the paper discusses the relationship between gold, money and derivatives, rejecting their notion that derivatives are some kind of new ‘commodity money’. An important theme absent from Bryan and Rafferty’s analysis is the relationship of financial trading and derivatives markets to parasitism in the imperialist world economy. To illustrate this, the paper notes advantages enjoyed by the major financial powers – the US and the UK – that are the main centres for the origination of derivatives and for derivatives trading.

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6

Attou, Samira, Ludovic Mignot, and Djelloul Ziadi. "Bottom-Up derivatives of tree expressions." RAIRO - Theoretical Informatics and Applications 55 (2021): 4. http://dx.doi.org/10.1051/ita/2021008.

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In this paper, we extend the notion of (word) derivatives and partial derivatives due to (respectively) Brzozowski and Antimirov to tree derivatives using already known inductive formulae of quotients. We define a new family of extended regular tree expressions (using negation or intersection operators), and we show how to compute a Brzozowski-like inductive tree automaton; the fixed point of this construction, when it exists, is the derivative tree automaton. Such a deterministic tree automaton can be used to solve the membership test efficiently: the whole structure is not necessarily computed, and the derivative computations can be performed in parallel. We also show how to solve the membership test using our (Bottom-Up) partial derivatives, without computing an automaton.

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7

LILLO, R. E., and M. MARTIN. "Characterization Results Based on a Functional Derivative Approach." Combinatorics, Probability and Computing 10, no. 5 (September 2001): 417–34. http://dx.doi.org/10.1017/s0963548301004825.

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We introduce a notion of the derivative with respect to a function, not necessarily related to a probability distribution, which generalizes the concept of derivative as proposed by Lebesgue [14]. The differential calculus required to solve linear differential equations using this notion of the derivative is included in the paper. The definition given here may also be considered as the inverse operator of a modified notion of the Riemann–Stieltjes integral. Both this unified approach and the results of differential calculus allow us to characterize distributions in terms of three different types of conditional expectations. In applying these results, a test of goodness of fit is also indicated. Finally, two characterizations of a general Poisson process are included. Specifically, a useful result for the homogeneous Poisson process is generalized.

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8

Muslikh, Mohamad, Adem Kilicman, Siti Hasana bt Sapar, and Norfifah bt Bachoklati. "The metric derivative of set-valued functions." Advances in Pure and Applied Mathematics 10, no. 3 (July 1, 2019): 263–72. http://dx.doi.org/10.1515/apam-2018-0028.

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Abstract In this article, we introduce the notion of “metrically differentiable” for set-valued functions. By using this notion, it is shown that each Lipschitz set-valued function is differentiable almost everywhere. Its relationship to the differentiation in the sense of Hukuhara and its generalizations are also discussed.

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9

Torre, Davide La. "NECESSARY OPTIMALITY CONDITIONS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS." Mathematical Modelling and Analysis 8, no. 2 (June 30, 2003): 165–74. http://dx.doi.org/10.3846/13926292.2003.9637221.

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In this paper we introduce a notion of generalized derivative for nonsmooth vector functions in order to obtain necessary optimality conditions for vector optimization problems. This definition generalizes to the vector case the notion introduced by Michel and Penot and extended by Yang and Jeyakumar. This generalized derivative is contained in the Clarke subdifferential and then the corresponding optimality conditions are sharper than the Clarke's ones.

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10

Korniłowicz, Artur. "Differentiability of Polynomials over Reals." Formalized Mathematics 25, no. 1 (March 28, 2017): 31–37. http://dx.doi.org/10.1515/forma-2017-0002.

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Summary In this article, we formalize in the Mizar system [3] the notion of the derivative of polynomials over the field of real numbers [4]. To define it, we use the derivative of functions between reals and reals [9].

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11

Yakar, Coşkun. "Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference." Abstract and Applied Analysis 2010 (2010): 1–16. http://dx.doi.org/10.1155/2010/762857.

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The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial time difference stability of the perturbed fractional-order differential equation with respect to the unperturbed fractional-order differential equation.

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12

Atangana, Abdon, and S. C. Oukouomi Noutchie. "A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/498381.

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The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functionsuas function of time and space. The functionuaccounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer) in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.

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13

ANDRIANOV, A. A., M. V. IOFFE, F. CANNATA, and J. P. DEDONDER. "SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM." International Journal of Modern Physics A 10, no. 18 (July 20, 1995): 2683–702. http://dx.doi.org/10.1142/s0217751x95001261.

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In a search for pairs of quantum systems linked by dynamical symmetries, we give a systematic analysis of novel extensions of standard one-dimensional supersymmetric quantum mechanics. The most general supercharges involving higher order derivatives are introduced, leading to an algebra which incorporates a higher order polynomial of the Hamiltonian. We investigate the condition for irreducibility of such a higher order generator to a product of standard first derivative Darboux transformations. As a new example of application of this approach we study the quantum-mechanical radial problem including the scattering amplitudes. We also investigate the links between this higher derivative SUSY and a q-deformed supersymmetric quantum mechanics and introduce the notion of self-similarity in momentum space. An explicit model for the scattering amplitude is constructed in terms of a hypergeometric function which corresponds to a reflectionless potential with infinitely many bound states.

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14

Cherubini, C., S. Filippi, A. Gizzi, and M. G. C. Nestola. "On the Wall Shear Stress Gradient in Fluid Dynamics." Communications in Computational Physics 17, no. 3 (March 2015): 808–21. http://dx.doi.org/10.4208/cicp.030714.101014a.

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AbstractThe gradient of the fluid stresses exerted on curved boundaries, conventionally computed in terms of directional derivatives of a tensor, is here analyzed by using the notion of intrinsic derivative which represents the geometrically appropriate tool for measuring tensor variations projected on curved surfaces. Relevant differences in the two approaches are found by using the classical Stokes analytical solution for the slow motion of a fluid over a fixed sphere and a numerically generated three dimensional dynamical scenario. Implications for theoretical fluid dynamics and for applied sciences are finally discussed.

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15

Dotto, Emanuele. "EQUIVARIANT CALCULUS OF FUNCTORS AND-ANALYTICITY OF REAL ALGEBRAIC -THEORY." Journal of the Institute of Mathematics of Jussieu 15, no. 4 (April 1, 2015): 829–83. http://dx.doi.org/10.1017/s1474748015000067.

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We define a theory of Goodwillie calculus for enriched functors from finite pointed simplicial $G$-sets to symmetric $G$-spectra, where $G$ is a finite group. We extend a notion of $G$-linearity suggested by Blumberg to define stably excisive and ${\it\rho}$-analytic homotopy functors, as well as a $G$-differential, in this equivariant context. A main result of the paper is that analytic functors with trivial derivatives send highly connected $G$-maps to $G$-equivalences. It is analogous to the classical result of Goodwillie that ‘functors with zero derivative are locally constant’. As the main example, we show that Hesselholt and Madsen’s Real algebraic $K$-theory of a split square zero extension of Wall antistructures defines an analytic functor in the $\mathbb{Z}/2$-equivariant setting. We further show that the equivariant derivative of this Real $K$-theory functor is $\mathbb{Z}/2$-equivalent to Real MacLane homology.

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16

SIUDUT, STANISLAW. "ON THE DENJOY-PERRON-BOCHNER INTEGRAL." Tamkang Journal of Mathematics 25, no. 4 (December 1, 1994): 295–300. http://dx.doi.org/10.5556/j.tkjm.25.1994.4457.

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The notion of Denjoy integrals of abstract functions was first intro- duced by A. Alexiewicz [1]. His descriptive definitions are based upon a concept of the approximate derivative. In this paper we present another descriptive definition for the Denjoy-Perron integral of abstract functions - via the parametric derivative of Tolstov [8]. Some properties of this integral are examined.

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17

Helfer, A. D. "Spinor Lie derivatives and Fermion stress–energies." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2186 (February 2016): 20150757. http://dx.doi.org/10.1098/rspa.2015.0757.

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Stress–energies for Fermi fields are derived from the principle of general covariance. This is done by developing a notion of Lie derivatives of spinors along arbitrary vector fields. A substantial theory of such derivatives was first introduced by Kosmann; here, I show how an apparent conflict in the literature on this is due to a difference in the definitions of spinors, and that tracking the Lie derivative of the Infeld–van der Waerden symbol, as well as the spinor fields under consideration, gives a fuller picture of the geometry and leads to the Fermion stress–energy. The differences in the definitions of spinors do not affect the results here, but could matter in certain quantum-gravity programs and for spinor transformations under discrete symmetries.

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18

MANTACI, ROBERTO, SABRINA MANTACI, and ANTONIO RESTIVO. "BALANCE PROPERTIES AND DISTRIBUTION OF SQUARES IN CIRCULAR WORDS." International Journal of Foundations of Computer Science 21, no. 04 (August 2010): 647–64. http://dx.doi.org/10.1142/s0129054110007477.

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We study balance properties of circular words over alphabets of size greater than two. We give some new characterizations of balanced words connected to the Kawasaki-Ising model and to the notion of derivative of a word. Moreover we consider two different generalizations of the notion of balance, and we find some relations between them. Some of our results can be generalized to non periodic infinite words as well.

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19

Georgiev, Svetlin G., Vahid Darvish, and Tahere A. Roushan. "Some inequalities for exponentially convex functions on time scales." Mathematica Slovaca 71, no. 4 (August 1, 2021): 925–40. http://dx.doi.org/10.1515/ms-2021-0031.

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Abstract In this paper, we introduce the notion of exponentially convex functions on time scales and then we establish Hermite-Hadamard type inequalities for this class of functions. As special case, we derive this double inequality in the context of classical notion of exponentially convex functions and convex functions. Moreover, we prove some new integral inequalities for n-times continuously differentiable functions with exponentially convex first Δ-derivative.

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20

McAnally, Mary Lea. "Banks, Risk, and FAS105 Disclosures." Journal of Accounting, Auditing & Finance 11, no. 3 (July 1996): 453–90. http://dx.doi.org/10.1177/0148558x9601100313.

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This study examines whether Statement of Financial Accounting Standard No. 105 (FAS105) footnote disclosures of off-balance-sheet financial instruments and derivatives provide risk-relevant information in addition to that provided by the balance sheet alone. A theoretical model relates market and industry risk measures to FAS105 disclosures. Empirical tests of the model reveal that these disclosures do provide risk-relevant numbers although the results are not uniformly strong. The balance sheet financial instruments explain 42 percent of the variation in market risk and 45 percent of the variation in industry-level risk among 499 U.S. commercial bank holding companies. FAS105 disclosures of off-balance-sheet instruments and derivative positions explain an additional 5 to 7 percent of the variation. Stronger evidence is presented that shows that certain controversial classes of derivatives are not associated with increased levels of market and industry-level risk. This latter evidence stands in contrast to the current notion that derivative contracts, especially interest rate and currency swaps, increase overall bank riskiness. Results also corroborate the FASB categorization of classes of financial instruments along two important risk dimensions: credit risk and market risk.

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21

WU, LIXIN, and DAWEI ZHANG. "xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT." International Journal of Theoretical and Applied Finance 23, no. 01 (February 2020): 2050006. http://dx.doi.org/10.1142/s0219024920500065.

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xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

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22

Caputo, Michele, and Mauro Fabrizio. "On the notion of fractional derivative and applications to the hysteresis phenomena." Meccanica 52, no. 13 (March 13, 2017): 3043–52. http://dx.doi.org/10.1007/s11012-017-0652-y.

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23

Bosede, Fagbemigun Opeyemi, and Adesanmi A. Mogbademu. "SOME CLASSES OF CONVEX FUNCTIONS ON TIME SCALES." Facta Universitatis, Series: Mathematics and Informatics 35, no. 1 (April 6, 2020): 011. http://dx.doi.org/10.22190/fumi2001011b.

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We have introduced diamond $\phi_{h-s, \mathbb{T}}$ derivative and diamond $\phi_{h-s,\mathbb{T}}$ integral on an arbitrary time scale. Moreover, various interconnections with the notion of classes of convex functions about these new concepts are also discussed.

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24

El-Nabulsi, Rami Ahmad. "Modified field equations from a complexified nonlocal metric." Canadian Journal of Physics 97, no. 8 (August 2019): 816–27. http://dx.doi.org/10.1139/cjp-2018-0168.

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We argue that it is possible to obtain higher-derivative Einstein’s field equations by means of an extended complexified backward–forward nonlocal extension of the space–time metric, which depends on space–time vectors. Our approach generalizes the notion of the covariant derivative along tangent vectors of a given manifold, and accordingly many of the differential geometrical operators and symbols used in general relativity. Equations of motion are derived and a nonlocal complexified general relativity theory is formulated. A number of illustrations are proposed and discussed accordingly.

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25

Balachandran, Krishnan, and Shanmugam Divya. "Controllability of nonlinear implicit fractional integrodifferential systems." International Journal of Applied Mathematics and Computer Science 24, no. 4 (December 1, 2014): 713–22. http://dx.doi.org/10.2478/amcs-2014-0052.

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Abstract In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo’s fixed point theorem. Examples are included to verify the result.

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26

García, F., and M. A. Melguizo Padial. "Paratingent Derivative Applied to the Measure of the Sensitivity in Multiobjective Differential Programming." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/812125.

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We analyse the sensitivity of differential programs of the form subject to where and are maps whose respective images lie in ordered Banach spaces. Following previous works on multiobjective programming, the notion of -optimal solution is used. The behaviour of some nonsingleton sets of -optimal solutions according to changes of the parameter in the problem is analysed. The main result of the work states that the sensitivity of the program is measured by a Lagrange multiplier plus a projection of its derivative. This sensitivity is measured by means of the paratingent derivative.

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27

Van Fraassen, Bas C. "Probabilité conditionnelle et certitude." Dialogue 36, no. 1 (1997): 69–90. http://dx.doi.org/10.1017/s0012217300009306.

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AbstractPersonal probability is now a familiar subject in epistemology, together with such more venerable notions as knowledge and belief. But there are severe strains between probability and belief; if either is taken as the more basic, the other may suffer. After explaining the difficulties of attempts to accommodate both, I shall propose a unified account which takes conditional personal probability as basic. Full belief is therefore a defined, derivative notion. Yet we will still be able to picture opinion as follows: my subjective probability is only a grading of the possibilities left open by my beliefs. My conditional probabilities generally derive — in a sense to be explicated — from the strongest belief I can maintain when admitting the relevant condition.

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28

Panero, Monica, Ferdinando Arzarello, and Cristina Sabena. "The Mathematical Work with the Derivative of a Function: Teachers’ Practices with the Idea of “Generic”." Bolema: Boletim de Educação Matemática 30, no. 54 (April 2016): 265–86. http://dx.doi.org/10.1590/1980-4415v30n54a13.

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Abstract This paper investigates the introduction of the derivative notion and, specifically, the introduction of the derivative function, as a significant moment in the development of mathematical work on functions. In particular, we analyse the process of genericization that two Italian teachers conducted with their grade 13 students, in order to make them shift from the derivative at a specific point x0to the derivative as a global function in the x variable. Specifically, we analyse the role of the teacher in the semiotic genesis of this process and investigate the role of semiotic resources therein. As a result, we highlight the importance of conducting carefully this shift from the pointwise x0 sign to the global x sign, in order to gain an actual shift in the perceived properties of the derivative function, which depends on the x sign as a variable. In conclusion, we connect our findings to the model of the Mathematical Working Space of functions, with particular regard to the “visualisation” process and the semiotic axis.

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29

ISIDRO, JOSÉ M. "WIGNER FUNCTIONS, FRESNEL OPTICS, AND SYMPLECTIC CONNECTIONS ON PHASE SPACE." International Journal of Geometric Methods in Modern Physics 05, no. 05 (August 2008): 663–76. http://dx.doi.org/10.1142/s0219887808003089.

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We prove that Wigner functions contain a symplectic connection. The latter covariantizes the symplectic exterior derivative on phase space. We analyze the role played by this connection and introduce the notion of local symplectic covariance of quantum-mechanical states. This latter symmetry is at work in the Schrödinger equation on phase space.

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30

Rashid, Saima, Rehana Ashraf, Ahmet Ocak Akdemir, Manar A. Alqudah, Thabet Abdeljawad, and Mohamed S. Mohamed. "Analytic Fuzzy Formulation of a Time-Fractional Fornberg–Whitham Model with Power and Mittag–Leffler Kernels." Fractal and Fractional 5, no. 3 (September 8, 2021): 113. http://dx.doi.org/10.3390/fractalfract5030113.

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This manuscript assesses a semi-analytical method in connection with a new hybrid fuzzy integral transform and the Adomian decomposition method via the notion of fuzziness known as the Elzaki Adomian decomposition method (briefly, EADM). Moreover, we use the aforesaid strategy to address the time-fractional Fornberg–Whitham equation (FWE) under gH-differentiability by employing different initial conditions (IC). Several algebraic aspects of the fuzzy Caputo fractional derivative (CFD) and fuzzy Atangana–Baleanu (AB) fractional derivative operator in the Caputo sense, with respect to the Elzaki transform, are presented to validate their utilities. Apart from that, a general algorithm for fuzzy Caputo and AB fractional derivatives in the Caputo sense is proposed. Some illustrative cases are demonstrated to understand the algorithmic approach of FWE. Taking into consideration the uncertainty parameter ζ∈[0,1] and various fractional orders, the convergence and error analysis are reported by graphical representations of FWE that have close harmony with the closed form solutions. It is worth mentioning that the projected approach to fuzziness is to verify the supremacy and reliability of configuring numerical solutions to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

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31

KITTLE, SIMON. "Heavenly freedom, derivative freedom, and the value of free choices." Religious Studies 56, no. 4 (October 16, 2018): 455–72. http://dx.doi.org/10.1017/s0034412518000689.

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AbstractSennett (1999) and Pawl and Timpe (2009; 2013) attempt to show how we can praise heavenly agents for things they inevitably do in heaven by appealing to the notion of derivative freedom. Matheson (2017) has criticized this use of derivative freedom. In this article I show why Matheson's argument is inconclusive but also how the basic point may be strengthened to undermine the use Sennett and Pawl and Timpe make of derivative freedom. I then show why Matheson is mistaken to claim that the value of free choice depends on an agent retaining the ability to change their mind; in so doing I demonstrate that some choices which result in fixed outcomes – a feature of the choices leading to impeccability – can indeed be valuable even if they cannot be undone.

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32

Laud, Peeter, Alisa Pankova, and Martin Pettai. "A Framework of Metrics for Differential Privacy from Local Sensitivity." Proceedings on Privacy Enhancing Technologies 2020, no. 2 (April 1, 2020): 175–208. http://dx.doi.org/10.2478/popets-2020-0023.

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AbstractThe meaning of differential privacy (DP) is tightly bound with the notion of distance on databases, typically defined as the number of changed rows. Considering the semantics of data, this metric may be not the most suitable one, particularly when a distance comes out as larger than the data owner desired (which would undermine privacy). In this paper, we give a mechanism to specify continuous metrics that depend on the locations and amounts of changes in a much more nuanced manner. Our metrics turn the set of databases into a Banach space. In order to construct DP information release mechanisms based on our metrics, we introduce derivative sensitivity, an analogue to local sensitivity for continuous functions. We use this notion in an analysis that determines the amount of noise to be added to the result of a database query in order to obtain a certain level of differential privacy, and demonstrate that derivative sensitivity allows us to employ powerful mechanisms from calculus to perform the analysis for a variety of queries. We have implemented the analyzer and evaluated its efficiency and precision.

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33

Aron, Richard M., and Pablo Galindo. "Weakly compact multilinear mappings." Proceedings of the Edinburgh Mathematical Society 40, no. 1 (February 1997): 181–92. http://dx.doi.org/10.1017/s0013091500023543.

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The notion of Arens regularity of a bilinear form on a Banach space E is extended to continuous m-linear forms, in such a way that the natural associated linear mappings, E→L (m−1E) and (m – l)-linear mappings E × … × E → E', are all weakly compact. Among other applications, polynomials whose first derivative is weakly compact are characterized.

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34

Schenkel, Alexander. "Module parallel transports in fuzzy gauge theory." International Journal of Geometric Methods in Modern Physics 11, no. 03 (March 2014): 1450021. http://dx.doi.org/10.1142/s0219887814500212.

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In this paper, we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct for every derivation X a module parallel transport, which is a lift to the module of the one-parameter group of algebra automorphisms generated by X. This parallel transport morphism is determined uniquely by an ordinary differential equation depending on the covariant derivative along X. Based on these parallel transport morphisms, we define a basic set of gauge invariant observables, i.e. functions from the space of connections to the complex numbers. For modules equipped with a Hermitian structure, we prove that this set of observables is separating on the space of gauge equivalence classes of Hermitian connections. This solves the gauge copy problem for fuzzy gauge theories.

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TÉLLEZ-SÁNCHEZ, GAMALIEL YAFTE, and JUAN BORY-REYES. "GENERALIZED ITERATED FUNCTION SYSTEMS ON HYPERBOLIC NUMBER PLANE." Fractals 27, no. 04 (June 2019): 1950045. http://dx.doi.org/10.1142/s0218348x19500452.

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Iterated function systems provide the most fundamental framework to create many fascinating fractal sets. They have been extensively studied when the functions are affine transformations of Euclidean spaces. This paper investigates the iterated function systems consisting of affine transformations of the hyperbolic number plane. We show that the basics results of the classical Hutchinson–Barnsley theory can be carried over to construct fractal sets on hyperbolic number plane as its unique fixed point. We also discuss about the notion of hyperbolic derivative of an hyperbolic-valued function and then we use this notion to get some generalization of cookie-cutter Cantor sets in the real line to the hyperbolic number plane.

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Aze, D. "An inversion theorem for set-valued maps." Bulletin of the Australian Mathematical Society 37, no. 3 (June 1988): 411–14. http://dx.doi.org/10.1017/s0004972700027027.

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The aim of this paper is to give an inversion theorem for set-valued maps involving both some known results for functions and set-valued maps. To do this we introduce a notion of strict differentiability for set-valued maps and we use a Newton like method assuming the derivative to be surjective. Moreover we prove the pseudo-Lipschitz regularity of the inverse.

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Štícha, František. "K Pojmu Slovotvorné Solitérnosti." Journal of Linguistics/Jazykovedný casopis 69, no. 3 (December 1, 2018): 581–88. http://dx.doi.org/10.2478/jazcas-2019-0034.

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Abstract This paper focuses on different types of wordformation uniqueness. Wordformation uniqueness can be found in solitary wordformation structures, which the author defines as unique structures representing a specific wordformation type found in a single derivative. The basic and simplest type is represented by a unique affix in a single derivative in the respective language of a given time period. An example of this is the Czech noun obličej [‘face’]: the circumfix ob-ej (with -lič- as a radix to be found in the noun líce [‘cheek’]) is found in no other noun in the contemporary Czech. Another uniquely formed noun in contemporary Czech is the noun rukáv [‘sleeve’], derived from ruka [‘hand’] with the unique suffix -áv. Specific wordformation solitaires are theoretically conceived values. They are derivatives with a specific, but not uniquely found affix which is uniquely added to the stem of a single word of a specific part of speech, e.g. the very specific suffix -ule is added to the stem of the verb vrtět [‘to wag’] so that the noun vrtule [‘propeller’] is derived. This article shows that the notion of wordformation solitariness can be theoretically postulated on different levels of abstractness, both of the form and of the wordformation meaning.

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Kamalapurkar, Rushikesh, Warren E. Dixon, and Andrew R. Teel. "On reduction of differential inclusions and Lyapunov stability." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 24. http://dx.doi.org/10.1051/cocv/2019074.

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In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is pointwise smaller (in the sense of set containment) than the original set-valued map. The corresponding reduced differential inclusion, defined by the reduced set-valued map, is utilized to develop a generalized notion of a derivative for locally Lipschitz candidate Lyapunov functions in the direction(s) of a set-valued map. The developed generalized derivative yields less conservative statements of Lyapunov stability theorems, invariance theorems, invariance-like results, and Matrosov theorems for differential inclusions. Included illustrative examples demonstrate the utility of the developed theory.

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Bershadsky, M. "THE SUPERBRANCH POINTS AND TWO-LOOP CORRECTION IN THE HETEROTIC STRING THEORY." Modern Physics Letters A 03, no. 01 (January 1988): 91–108. http://dx.doi.org/10.1142/s0217732388000131.

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In this paper we discuss the notion of superbranch point. The conformal field simulating the superbranch point is constructed. Using this field we construct the two-loop correction in the heterotic string theories (for the theories with gauge groups SO (32) and E8×E8). The contribution from different spin structures cancel each other but only up to the total derivative over the moduli space.

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EL BASRAOUI, ABDELKRIM, and ABDELLAH SEBBAR. "RATIONAL EQUIVARIANT FORMS." International Journal of Number Theory 08, no. 04 (May 16, 2012): 963–81. http://dx.doi.org/10.1142/s1793042112500571.

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We investigate the notion of equivariant forms as functions on the upper half-plane commuting with the action of a discrete group. We put an emphasis on the rational equivariant forms for a modular subgroup that are parametrized by generalized modular forms. Furthermore, we study this parametrization when the modular subgroup is of genus zero as well as their behavior under the effect of the Schwarz derivative.

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TAIVĀNE, ELIZABETE. "MULTI-RELIGIOUS BELONGING AND CHRISTIAN IDENTITY IN THE WEST: CONTEXTS AND PERSPECTIVES." Study of Religion, no. 2 (2021): 87–96. http://dx.doi.org/10.22250/2072-8662.2021.2.87-96.

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Double and multiple religious belonging (MRB) is one of the most popular fields of research in Religious Studies and Theology in the West. It is curious that Russia does not utilize the notion of MRB being acquainted just with the notion of double belief (Rus. dvoeverie ). The latter has almost nothing in common with double and multiple religious belonging in the Western sense of the word. So, what is MRB? Although the term does not seem to be ambiguous it does not mean a complete form of belonging to two or more religious traditions, it rather implies formal belonging to one religion and some extent of fragmentary participation in another religion or other ones. The notion of MRB is linked to the postmodern contextual interpretation of religion beyond any essentialism, which allows speaking about the hybridity of religions and religion as such, as well as about the option to relativize or broaden the notion of Christian identity. What interreligious models allow to make use of the notion of MRB and how can MRB co-exist with Christian identity in its traditional exclusivist understanding? In the protestant environment, the notion of MRB is a derivative of pluralism whereas inside Roman Catholicism it collaborates with inclusivism, which in its turn tries to restrict itself to the performative aspect of foreign religions...

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CHAMPARNAUD, J. M., and D. ZIADI. "FROM C-CONTINUATIONS TO NEW QUADRATIC ALGORITHMS FOR AUTOMATON SYNTHESIS." International Journal of Algebra and Computation 11, no. 06 (December 2001): 707–35. http://dx.doi.org/10.1142/s0218196701000772.

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Two classical non-deterministic automata recognize the language denoted by a regular expression: the position automaton which deduces from the position sets defined by Glushkov and McNaughton–Yamada, and the equation automaton which can be computed via Mirkin's prebases or Antimirov's partial derivatives. Let |E| be the size of the expression and ‖E‖ be its alphabetic width, i.e. the number of symbol occurrences. The number of states in the equation automaton is less than or equal to the number of states in the position automaton, which is equal to ‖E‖+1. On the other hand, the worst-case time complexity of Antimirov algorithm is O(‖E‖3· |E|2), while it is only O(‖E‖·|E|) for the most efficient implementations yielding the position automaton (Brüggemann–Klein, Chang and Paige, Champarnaud et al.). We present an O(|E|2) space and time algorithm to compute the equation automaton. It is based on the notion of canonical derivative which makes it possible to efficiently handle sets of word derivatives. By the way, canonical derivatives also lead to a new O(|E|2) space and time algorithm to construct the position automaton.

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Grabisch, Michel, and Christophe Labreuche. "Derivative of functions over lattices as a basis for the notion of interaction between attributes." Annals of Mathematics and Artificial Intelligence 49, no. 1-4 (June 16, 2007): 151–70. http://dx.doi.org/10.1007/s10472-007-9052-7.

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MAJEED, JAVED. "THE CRISIS OF SECULARISM IN INDIA." Modern Intellectual History 7, no. 3 (September 30, 2010): 653–66. http://dx.doi.org/10.1017/s1479244310000284.

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In the early 1960s, Donald Smith's India as a Secular State questioned the credentials of the Indian state's secularism. Since then the issue of what constitutes secularism in India has loomed large in Indian political thought. Like a number of other key categories in political history, such as nationalism, the debate has centred on the question whether the Indian state's version of secularism is viable in its own right or not, and if it is viable, whether it extends the concept of secularism in new and innovative directions. The other possibility is to see this secularism as a “derivative discourse” (to adopt a phrase from Partha Chatterjee), confusedly echoing Western notions of secularism, with the caste and communal complexities of Indian society and the structuring role of religion in everyday life at odds with any coherent or recognisable notion of secularism.

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Cross, Donald. "The Vigil of Philosophy: Derrida on Anachrony." Derrida Today 8, no. 2 (November 2015): 175–92. http://dx.doi.org/10.3366/drt.2015.0109.

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This paper orchestrates various moments in which Derrida makes recourse to the notion of anachrony – in analyses of khōra and demiurgic creation in the Timaeus and of the trace in Husserl – in order to describe a structural law according to which philosophy attempts to determine some ‘thing’ with the very categories that it makes possible and that are therefore structurally derivative, both too early and too late, in a word, anachronous.

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Casado-Díaz, Juan, and Inmaculada Gayte. "A derivation theory for generalized Besicovitch spaces and its application for partial differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 2 (April 2002): 283–315. http://dx.doi.org/10.1017/s0308210500001633.

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We present an extension of Besicovitch spaces, which has its origin in the works of Zhikov et al. and Kozlov and Oleinik. We show that these spaces have a similar behaviour to the Lp spaces, and we give a notion of derivative that allows us to treat partial differential problems in this frame. To the best of our knowledge, this is new, even for the usual Besicovitch spaces.

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Banič, Iztok. "Integrations on rings." Open Mathematics 15, no. 1 (April 1, 2017): 365–73. http://dx.doi.org/10.1515/math-2017-0034.

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Abstract In calculus, an indefinite integral of a function f is a differentiable function F whose derivative is equal to f. The main goal of the paper is to generalize this notion of the indefinite integral from the ring of real functions to any ring. We also investigate basic properties of such generalized integrals and compare them to the well-known properties of indefinite integrals of real functions.

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Damiá, Elena, Deborah Chicharro, Mónica Rubio, José Carrillo, Joaquín Sopena, Belén Cuervo, Sergio López, and José Vilar. "Can Plasma Rich in Growth Factors Be Safe for Parental Use? A Safety Study in the Canine Model." International Journal of Molecular Sciences 19, no. 9 (September 11, 2018): 2701. http://dx.doi.org/10.3390/ijms19092701.

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Low invasiveness is the main goal of modern surgery. The use of platelet-rich plasma (PRP) is known to be effective in a variety of applications, such as oral, maxillofacial, orthopedic, dermatologic and cosmetic surgeries. However, a potential ergogenic and carcinogenic effect of PRP derivatives by means of the insulin-like growth factor-1 (IGF-1) pathway has been suggested. Because of this notion, the purpose of this study is to assess the effect of a commercially available PRP-derivative intramuscular injection in the lumbar muscular tissue (local effect) and to determine the IGF-1 blood concentration (systemic effect) on healthy beagle dogs. Local effect was evaluated by computed tomography (CT) scan and echography, and systemic effect was calculated by blood testing on days 0, 14, 28, 42 and 56. No statistically significant changes were observed; thus, PRGF could be considered safe when using therapeutic doses.

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Richard, Mark. "What are Propositions?" Canadian Journal of Philosophy 43, no. 5-6 (December 2013): 702–19. http://dx.doi.org/10.1080/00455091.2013.870738.

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This paper defends the view that propositions – that is, what are picked about by complement clauses and the range of quantifiers like that in ‘Sanna believes all that Matti said’ – are states of affairs. States of affairs – and thus propositions – are not, in the primary sense, representational; what is representational and what is true or false in the first instance are mental states and sentence tokens that represent propositions. There is, it is argued, a derivative sense in which propositions are bearers of truth, but truth in that sense is a derivative, non-explanatory notion. This view is contrasted with views like the one Scott Soames develops in What is Meaning?. It’s argued that this view is superior to Soames’ in various ways.

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Fenn, Roger, and Denis Sjerve. "Massey Products and Lower Central Series of Free Groups." Canadian Journal of Mathematics 39, no. 2 (April 1, 1987): 322–37. http://dx.doi.org/10.4153/cjm-1987-015-5.

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The purpose of this paper is to continue the investigation into the relationships amongst Massey products, lower central series of free groups and the free differential calculus (see [4], [9], [12]). In particular we set forth the notion of a universal Massey product ≪α1, …, αk≫, where the αi are one dimensional cohomology classes. This product is defined with zero indeterminacy, natural and multilinear in its variables.In order to state the results we need some notation. Throughout F will denote the free group on fixed generators x1, …, xn andwill denote the lower central series of F. If I = (i1, …, ik) is a sequence such that 1 ≦ i1, …, ik ≦ n then ∂1 is the iterated Fox derivative and , where is the augmentation. By convention we set ∂1 = identity if I is empty.

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