Relevant bibliographies by topics / K)-Symmetric functions

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Academic literature on the topic 'K)-Symmetric functions'

Author: Grafiati
Published: 3 June 2025
Last updated: 6 July 2025

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Journal articles on the topic "K)-Symmetric functions"

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Anh, V. V. "K-Fold symmetric starlike univalent functions." Bulletin of the Australian Mathematical Society 32, no. 3 (1985): 419–36. http://dx.doi.org/10.1017/s0004972700002537.

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This paper establishes the radius of convexity, distortion and covering theorems for the classwhere−1 ≤ B < A ≤ 1, w(0) = 0, |w (z)| < 1 in the unit disc. Coefficient bounds for functions in are also derived.
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Calderón-Gómez, José E., Luis A. Medina, and Carlos A. Molina-Salazar. "Short k-rotation symmetric Boolean functions." Discrete Applied Mathematics 343 (January 2024): 49–64. http://dx.doi.org/10.1016/j.dam.2023.10.003.

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Asakly, Walaa. "Enumerating symmetric and non-symmetric peaks in words." Online Journal of Analytic Combinatorics, no. 13 (December 31, 2018): 1–7. https://doi.org/10.61091/ojac-1302.

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Let \([k] = \{1, 2, \ldots, k\}\) be an alphabet over \(k\) letters. A word \(\omega\) of length \(n\) over alphabet \([k]\) is an element of \([k]^n\) and is also called \(k\)-ary word of length \(n\). We say that \(\omega\) contains a peak, if exists \(2 \leq i \leq n-1\) such that \(\omega_{i-1} < \omega_i, \omega_i > \omega_{i+1}\). We say that \(\omega\) contains a symmetric peak, if exists \(2 \leq i \leq n-1\) such that \(\omega_{i-1} = \omega_{i+1} < \omega_i\), and contains a non-symmetric peak, otherwise. In this paper, we find an explicit formula for the generating functions for the number of \(k\)-ary words of length \(n\) according to the number of symmetric peaks and non-symmetric peaks in terms of Chebyshev polynomials of the second kind. Moreover, we find the number of symmetric and non-symmetric peaks in \(k\)-ary word of length \(n\) in two ways by using generating functions techniques, and by applying probabilistic methods.
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Rupp, R., та A. Sasane. "Reducibility in Aℝ(K), Cℝ(K), and A(K)". Canadian Journal of Mathematics 62, № 3 (2010): 646–67. http://dx.doi.org/10.4153/cjm-2010-025-9.

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AbstractLet K denote a compact real symmetric subset of ℂ and let Aℝ(K) denote the real Banach algebra of all real symmetric continuous functions on K that are analytic in the interior K◦ of K, endowed with the supremum norm. We characterize all unimodular pairs ( f , g) in Aℝ(K)2 which are reducible. In addition, for an arbitrary compact K in ℂ, we give a new proof (not relying on Banach algebra theory or elementary stable rank techniques) of the fact that the Bass stable rank of A(K) is 1. Finally, we also characterize all compact real symmetric sets K such that Aℝ(K), respectively Cℝ(K), has Bass stable rank 1.
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SERGEEV, A. N., and A. P. VESELOV. "JACK–LAURENT SYMMETRIC FUNCTIONS FOR SPECIAL VALUES OF PARAMETERS." Glasgow Mathematical Journal 58, no. 3 (2015): 599–616. http://dx.doi.org/10.1017/s0017089515000361.

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AbstractWe consider the Jack–Laurent symmetric functions for special values of parametersp0=n+k−1m, wherekis not rational andmandnare natural numbers. In general, the coefficients of such functions may have poles at these values ofp0. The action of the corresponding algebra of quantum Calogero–Moser integrals$\mathcal{D}$(k,p0) on the space of Laurent symmetric functions defines the decomposition into generalised eigenspaces. We construct a basis in each generalised eigenspace as certain linear combinations of the Jack–Laurent symmetric functions, which are regular atp0=n+k−1m, and describe the action of$\mathcal{D}$(k,p0) in these eigenspaces.
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Liu, Hongli. "The Weight and Nonlinearity of 2-rotation Symmetric Cubic Boolean Function." Journal of Mathematics Research 7, no. 2 (2015): 187. http://dx.doi.org/10.5539/jmr.v7n2p187.

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The conceptions of $\chi$-value and K-rotation symmetric Boolean functions are introduced by Cusick. K-rotation symmetric Boolean functions are a special rotation symmetric functions, which are invariant under the $k-th$ power of $\rho$.In this paper, we discuss cubic 2-value 2-rotation symmetric Boolean function with $2n$ variables, which denoted by $F^{2n}(x^{2n})$. We give the recursive formula of weight of $F^{2n}(x^{2n})$, and prove that the weight of $F^{2n}(x^{2n})$ is the same as its nonlinearity.
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Zhang, Z. Q., and Y. Y. Shi. "Communication complexities of symmetric XOR functions." Quantum Information and Computation 9, no. 3&4 (2009): 255–63. http://dx.doi.org/10.26421/qic9.3-4-5.

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We call $F:\{0, 1\}^n\times \{0, 1\}^n\to\{0, 1\}$ a symmetric XOR function if for a function $S:\{0, 1, ..., n\}\to\{0, 1\}$, $F(x, y)=S(|x\oplus y|)$, for any $x, y\in\{0, 1\}^n$, where $|x\oplus y|$ is the Hamming weight of the bit-wise XOR of $x$ and $y$. We show that for any such function, (a) the deterministic communication complexity is always $\Theta(n)$ except for four simple functions that have a constant complexity, and (b) up to a polylog factor, both the error-bounded randomized complexity and quantum communication with entanglement complexity are $\Theta(r_0+r_1)$, where $r_0$ and $r_1$ are the minimum integers such that $r_0, r_1\leq n/2$ and $S(k)=S(k+2)$ for all $k\in[r_0, n-r_1)$.
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DELENCLOS, JONATHAN, and ANDRÉ LEROY. "NONCOMMUTATIVE SYMMETRIC FUNCTIONS AND W-POLYNOMIALS." Journal of Algebra and Its Applications 06, no. 05 (2007): 815–37. http://dx.doi.org/10.1142/s021949880700251x.

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Let K, S, D be a division ring, an endomorphism and a S-derivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Viète formula and decompositions of differential operators. W-polynomials show up naturally, their connections with P-independency, Vandermonde and Wronskian matrices are briefly studied. The different linear factorizations of W-polynomials are analyzed. Connections between the existence of LLCM of monic linear polynomials with coefficients in a ring and the left duo property are established at the end of the paper.
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Zainab, Saira, Mohsan Raza, Qin Xin, Mehwish Jabeen, Sarfraz Nawaz Malik, and Sadia Riaz. "On q-Starlike Functions Defined by q-Ruscheweyh Differential Operator in Symmetric Conic Domain." Symmetry 13, no. 10 (2021): 1947. http://dx.doi.org/10.3390/sym13101947.

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Motivated by q-analogue theory and symmetric conic domain, we study here the q-version of the Ruscheweyh differential operator by applying it to the starlike functions which are related with the symmetric conic domain. The primary aim of this work is to first define and then study a new class of holomorphic functions using the q-Ruscheweyh differential operator. A new class k−STqτC,D of k-Janowski starlike functions associated with the symmetric conic domain, which are defined by the generalized Ruscheweyh derivative operator in the open unit disk, is introduced. The necessary and sufficient condition for a function to be in the class k−STqτC,D is established. In addition, the coefficient bound, partial sums and radii of starlikeness for the functions from the class of k-Janowski starlike functions related with symmetric conic domain are included.
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Dib, Hacen. "K-Bessel functions in two variables." International Journal of Mathematics and Mathematical Sciences 2003, no. 14 (2003): 909–16. http://dx.doi.org/10.1155/s0161171203112057.

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The Bessel-Muirhead hypergeometric system (or0F1-system) in two variables (and three variables) is solved using symmetric series, with an explicit formula for coefficients, in order to express theK-Bessel function as a linear combination of the J-solutions. Limits of this method and suggestions for generalizations to a higher rank are discussed.
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Books on the topic "K)-Symmetric functions"

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Roe, John. Winding around: The winding number in topology, geometry, and analysis. American Mathematical Society, 2015.

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Gelaki, Shlomo, Dmitri Nikshych, Pavel Etingof, and Victor Ostrik. Tensor Categories. American Mathematical Society, 2016.

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Tensor categories. American Mathematical Society, 2015.

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Book chapters on the topic "K)-Symmetric functions"

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Lam, Thomas, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono, and Mike Zabrocki. "Stanley Symmetric Functions and Peterson Algebras." In k-Schur Functions and Affine Schubert Calculus. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0682-6_3.

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Girko, Vyacheslav L. "Canonical Equation K 27 for Normalized Spectral Functions of Random Symmetric Block Matrices." In Theory of Stochastic Canonical Equations. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0989-8_27.

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Girko, Vyacheslav L. "Stochastic Canonical Equation K 42 for Normalized Spectral Functions of Random Symmetric Matrices with Block Structure." In Theory of Stochastic Canonical Equations. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0989-8_42.

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Girko, Vyacheslav L. "Twenty Five Years of Stochastic Canonical Equation K 39 for Normalized Spectral Functions of Ace-Symmetric Matrices." In Theory of Stochastic Canonical Equations. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0989-8_39.

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Girko, Vyacheslav L. "Class of Direct Canonical Equations K 47 for Spectral Functions of Random Symmetric Banded Matrices and Jacobi Matrices." In Theory of Stochastic Canonical Equations. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0989-8_47.

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Girko, Vyacheslav L. "Canonical Equation K 28 for Normalized Spectral Functions of Random Symmetric Matrices with Identically Distributed Independent Blocks. Block Matrix Density. SS-Laws." In Theory of Stochastic Canonical Equations. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0989-8_28.

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Girko, Vyacheslav L. "Stochastic Canonical Equation K 4 for Symmetric Random Matrices with Infinitely Small Entries. Necessary and Sufficient Conditions for the Convergence of Normalized Spectral Functions." In Theory of Stochastic Canonical Equations. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0989-8_4.

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Nakamura, Hiroaki, and Densuke Shiraishi. "Landen’s Trilogarithm Functional Equation and $$\ell $$-Adic Galois Multiple Polylogarithms." In Springer Proceedings in Mathematics & Statistics. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-97-3778-9_8.

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Abstract The Galois action on the pro- $$\ell $$ ℓ étale fundamental groupoid of the projective line minus three points with rational base points gives rise to a non-commutative formal power series in two variables with $$\ell $$ ℓ -adic coefficients, called the $$\ell $$ ℓ -adic Galois associator. In the present paper, we focus on how Landen’s functional equation of trilogarithms and its $$\ell $$ ℓ -adic Galois analog can be derived algebraically from the $$S_3$$ S 3 -symmetry of the projective line minus three points. Twofold proofs of the functional equation will be presented, one is based on the chain rule for the associator power series and the other is based on Zagier’s tensor criterion devised in the framework of graded Lie algebras. In the course of the second proof, we are led to investigate $$\ell $$ ℓ -adic Galois multiple polylogarithms appearing as regular coefficients of the $$\ell $$ ℓ -adic Galois associator. As an application, we show an $$\ell $$ ℓ -adic Galois analog of Oi-Ueno’s functional equation between $$Li_{1,\dots ,1,2}(1-z)$$ L i 1 , ⋯ , 1 , 2 ( 1 - z ) and $$Li_k(z)$$ L i k ( z ) ’s $$(k=1,2,...)$$ ( k = 1 , 2 , . . . ) .
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Macdonald, I. G. "Zonal Polynomials." In Symmetric Functions and Hall Polynomials. Oxford University PressOxford, 1995. http://dx.doi.org/10.1093/oso/9780198534891.003.0007.

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Abstract For a subgroup K of G, the following conditions are equivalent: (a) the induced representation 1G K is multiplicity-free: (b) the algebra C(G, K) is commutative If these equivalent conditions are satisfied, the pair (G, K) is called a Gelfand pair.
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Macdonald, I. G. "Hall Polynomials." In Symmetric Functions and Hall Polynomials. Oxford University PressOxford, 1995. http://dx.doi.org/10.1093/oso/9780198534891.003.0002.

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Abstract Let o be a (commutative) discrete valuation ring, p its maximal ideal, k — o/p the residue field. Later we shall require k to be a finite field, but for the present this restriction is unnecessary. We shall be concerned with finite o-modules M, that is to say, modules M which possess a finite composition series, or equivalently finitely-generated o-modules M such that p’M=Q for some r>0. If k is finite, the finite o-modules are precisely those which have a finite number of elements.
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Conference papers on the topic "K)-Symmetric functions"

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Clausen, Michael, and Paul Hühne. "Linear Time Fourier Transforms of S n-k -invariant Functions on the Symmetric Group S n." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. ACM, 2017. http://dx.doi.org/10.1145/3087604.3087628.

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Sumalatha, P., R. B. Sharma, and M. Hari Priya. "The third Hankel determinant for starlike functions with respect to symmetric points subordinate to k-Fibonacci sequence." In THE 11TH NATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5112254.

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Jeong, Kyeong-Hoon, Jin-Seok Park, and Won-Jae Lee. "Free Vibration Analysis of a Simply Supported Rectangular Tank Partially Filled With a Liquid." In ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/pvp2010-25494.

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This paper presents a theoretical analysis for the hydroelastic vibration of a rectangular tank partially filled with an ideal liquid. The wet dynamic displacement of the tank is approximated by combining the orthogonal polynomials satisfying the simply supported boundary conditions, since the rectangular tank is composed of four rectangular plates. As the facing rectangular plates are geometrically identical, the vibration modes of the facing plates can be divided into two categories: symmetric modes and asymmetric modes with respect to the vertical centerlines of the plates. The liquid displacement potential satisfying the boundary conditions is derived and the wet dynamic modal functions of the four plates are expanded by the finite Fourier transformation for a compatibility requirement along the contacting surface between the tank and the liquid. The natural frequencies of the rectangular tank in the wet condition are calculated by using the Rayleigh-Ritz method. The proposed analytical method is verified by observing an excellent agreement with three-dimensional finite element analysis results.
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Rice, Perry R., Xiaoyi Wang, and Howard J. Carmichael. "Cross correlations between fluorescent and transmitted photons in single-atom cavity-enhanced absorption." In OSA Annual Meeting. Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.ms9.

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We study a single two-level atom interacting on resonance with a weakly driven optical cavity mode. In earlier work on this system we calculated the degree of second-order coherence, the optical spectrum, and the spectrum of squeezing for both the transmitted light and fluorescence out the sides of the cavity.1,2 We present results for the cross-correlation functions that determine joint probabilities for a photodetection in transmission (fluorescence) followed by a photodetection in fluorescence (transmission). We compute these correlation functions numerically for arbitrary values of the three rates that govern the system dynamics: the atomic decay rate γ to modes other than the cavity mode, the photon escape rate from the cavity 2K, and the atom-field coupling constant g. Analytical results provide insight for the following limits of the parameters: (1) the bad-cavity limit, κ/γ→∞,κ/g→∞,g2/κγ constant; (2) the atomic-loss limit, κ/γ→0,κ/g→0,γ/g constant; (3) the cavity-loss limit, γ/κ→0,γ/g→0,g/κ constant; and (4) the good-cavity limit, k/γ→0,k/g→0,g2/κγ constant. In the bad-cavity limit the cross-correlation functions are symmetric with respect to the order of detection in transmission and fluorescence; in general they are not symmetric.
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Jensen, Anna Lyhne, Claus Uhrenholt Jensen, Kristine Møllenbach Rasmussen, Simon Sand Nielsen, Henrik Sørensen, and Thomas Condra. "Validation of Guidelines for CFD Modelling of a Single Tube Row and In-Line Tube Bundles." In ASME 2013 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/fedsm2013-16529.

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This paper questions and improves commonly used guidelines for modelling a tube bundle in cross-flow at ReD = 3.4 · 104 and ReD = 1.1 · 105. Especially, when the locations of flow separation are of high interest. A major conclusion of this paper is that near-wall modelling (y+ < 5) is preferable and use of wall functions with y+ > 5 should be avoided in relation to flow separation behind tubes in cross-flow. CFD modelling of a tube bundle may be simplified with the use of symmetric or periodic boundary conditions to account for the full geometry. The present work reveals periodicity in vorticity formation between a double cylinder row, though the wake region behind a single cylinder row is neither characterised as in-phase nor reversed phase. Likewise, periodic boundary conditions may result in a modelling with large wake deflections for a full tube bundle. Furthermore, since there is no unequivocal answer to which turbulence model to apply for tubes in cross-flow, the RNG k-ε, Realizable k-ε, SST k-ω, and RSM turbulence models are tested and compared.
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Ouyang, Jian-quan. "Full Symmetric Function in Partial K-Valued Logic." In 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2008. http://dx.doi.org/10.1109/fskd.2008.169.

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Ren, Wei-Min. "Windage and Axial Friction Losses of High Speed Generator." In International Joint Power Generation Conference collocated with TurboExpo 2003. ASMEDC, 2003. http://dx.doi.org/10.1115/ijpgc2003-40078.

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Air-cooled generators have been fulfilling a wide range of applications recently. Concurrent with a low cost target, the market demands high efficiency and high performance designs. Windage and friction losses, caused by rotor rotation and cooling gas flowing through the ventilation circuits, represents one of the largest loss components in air-cooled generators. Carefully managing the windage and friction loss is critical to ensure the success of air-cooled generators. This work is motivated by development of air-cooled high-speed generators. In such applications, the flow inside the annular gap between the rotor and stator is highly turbulent. The flow characteristics are not fully understood. Physics-based correlations, which calculate the windage and friction losses, don’t exist in the literature. The purpose of this work is to develop such transfer functions for machine design. Numerical simulations, using commercial CFD code FLUENT 6.0 and Design of Experiment (DOE) method, have been carried out to study the flow characteristics in the annular space between the cylindrical rotor and stator. All simulations were performed using an axial-symmetric model, along with RNG k-ε turbulence model and enhanced wall treatment. In the study, the generator rated speed ranged from 5000 to 20000 rpm; the Taylor number ranged from 1750 to 78000; and the Mach number ranged from 0.25 to 1.0. The effect of axial flow on windage loss was carefully studied. Axial flow exhibited a strong impact on windage loss. The CFD results are rationalized. Transfer functions for windage and axial friction losses are created. They provide a better basis to explore the design space at the early stage of the product development.
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Lauer, Pascal, Alvaro Torralba, Daniel Fišer, Daniel Höller, Julia Wichlacz, and Jörg Hoffmann. "Polynomial-Time in PDDL Input Size: Making the Delete Relaxation Feasible for Lifted Planning." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/567.

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Polynomial-time heuristic functions for planning are commonplace since 20 years. But polynomial-time in which input? Almost all existing approaches are based on a grounded task representation, not on the actual PDDL input which is exponentially smaller. This limits practical applicability to cases where the grounded representation is "small enough". Previous attempts to tackle this problem for the delete relaxation leveraged symmetries to reduce the blow-up. Here we take a more radical approach, applying an additional relaxation to obtain a heuristic function that runs in time polynomial in the size of the PDDL input. Our relaxation splits the predicates into smaller predicates of fixed arity K. We show that computing a relaxed plan is still NP-hard (in PDDL input size) for K>=2, but is polynomial-time for K=1. We implement a heuristic function for K=1 and show that it can improve the state of the art on benchmarks whose grounded representation is large.
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Wang, Kuo-Hua, and Jia-Hung Chen. "K-disjointness paradigm with application to symmetry detection for incompletely specified functions." In the 2005 conference. ACM Press, 2005. http://dx.doi.org/10.1145/1120725.1120775.

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Lederer, Patrick. "Strategyproof Randomized Social Choice for Restricted Sets of Utility Functions." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/43.

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When aggregating preferences of multiple agents, strategyproofness is a fundamental requirement. For randomized voting rules, so-called social decision schemes (SDSs), strategyproofness is usually formalized with the help of utility functions. A classic result shown by Gibbard in 1977 characterizes the set of SDSs that are strategyproof with respect to all utility functions and shows that these SDSs are either indecisive or unfair. For finding more insights into the trade-off between strategyproofness and decisiveness, we propose the notion of U-strategyproofness which requires that only voters with a utility function in the set U cannot manipulate. In particular, we show that if the utility functions in U value the best alternative much more than other alternatives, there are U-strategyproof SDSs that choose an alternative with probability 1 whenever all but k voters rank it first. We also prove for rank-based SDSs that this large gap in the utilities is required to be strategyproof and that the gap must increase in k. On the negative side, we show that U-strategyproofness is incompatible with Condorcet-consistency if U satisfies minimal symmetry conditions and there are at least four alternatives. For three alternatives, the Condorcet rule can be characterized based on U-strategyproofness for the set U containing all equi-distant utility functions.
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