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Journal articles on the topic 'P-multiplier'

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Published: 4 June 2021

Last updated: 8 February 2022

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1

Hartmann, Andreas. "Pointwise multipliers in Hardy-Orlicz spaces, and interpolation." MATHEMATICA SCANDINAVICA 106, no. 1 (March 1, 2010): 107. http://dx.doi.org/10.7146/math.scand.a-15128.

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We study multipliers of Hardy-Orlicz spaces ${\mathcal H}_{\Phi}$ which are strictly contained between $\bigcup_{p>0}H^p$ and so-called "big" Hardy-Orlicz spaces. Big Hardy-Orlicz spaces, carrying an algebraic structure, are equal to their multiplier algebra, whereas in classical Hardy spaces $H^p$, the multipliers reduce to $H^{\infty}$. For Hardy-Orlicz spaces ${\mathcal H}_{\Phi}$ between these two extremal situations and subject to some conditions, we exhibit multipliers that are in Hardy-Orlicz spaces the defining functions of which are related to $\Phi$. In general it cannot be expected to obtain a characterization of the multiplier algebra in terms of Hardy-Orlicz spaces since these are in general not algebras. Nevertheless, some examples show that we are not very far from such a characterization. In certain situations we see how the multiplier algebra grows in a sense from $H^{\infty}$ to big Hardy-Orlicz spaces when we go from classical $H^p$ spaces to big Hardy-Orlicz spaces. However, the multiplier algebras are not always ordered as their underlying Hardy-Orlicz spaces. Such an ordering holds in certain situations, but examples show that there are large Hardy-Orlicz spaces for which the multipliers reduce to $H^{\infty}$ so that the multipliers do in general not conserve the ordering of the underlying Hardy-Orlicz spaces. We apply some of the multiplier results to construct Hardy-Orlicz spaces close to $\bigcup_{p>0}H^p$ and for which the free interpolating sequences are no longer characterized by the Carleson condition which is well known to characterize free interpolating sequences in $H^p$, $p>0$.

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2

Alkurwy, Salah. "A novel approach of multiplier design based on BCD decoder." Indonesian Journal of Electrical Engineering and Computer Science 14, no. 1 (April 1, 2019): 38. http://dx.doi.org/10.11591/ijeecs.v14.i1.pp38-43.

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<p><span>A novel approach of multiplier design is presented in this paper. The design </span>idea is implemented based on binary coded decimal (BCD) decoder to seven segment display, by computing all the probability of multiplying 3 3 binary digits bits and grouping in table rows. The obtaining of the combinational logic functions is achieved by simplified the generated columns of [A<sub>5: </sub>A<sub>0</sub>]<sub>, </sub>using a Karnaugh map. Then, the 3 3-bits multiplier circuit is used to implement the 6x6- and 12x 12-bit multipliers. Comparing with a conventional multiplier, the proposed design outperformed in terms of the time delay by a 32% and 41.8% respectively. It is also reduced the combinational adaptive look-up-tables (ALUTs) by 24.6%, and 46% for both multipliers. Both overmentioned advantages make the proposed multipliers more attractive and suitable for high-speed digital systems</p><p> </p><p> </p><p> </p><p> </p><p> </p><p> </p>

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3

BOSKO, LINDSEY R. "ON SCHUR MULTIPLIERS OF LIE ALGEBRAS AND GROUPS OF MAXIMAL CLASS." International Journal of Algebra and Computation 20, no. 06 (September 2010): 807–21. http://dx.doi.org/10.1142/s0218196710005881.

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The Lie algebra analogue to the Schur multiplier has been investigated in a number of recent articles. We consider the multipliers of Lie algebras of maximal class, classifying these algebras with a certain additional property. The classification leads to a conjecture about a bound on the dimension of the multiplier for each of these algebras and also for p-groups of maximal class. The conjectures are then shown to hold.

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4

Ellis, Graham, and James Wiegold. "A bound on the Schur multiplier of a prime-power group." Bulletin of the Australian Mathematical Society 60, no. 2 (October 1999): 191–96. http://dx.doi.org/10.1017/s0004972700036327.

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The paper improves on an upper bound for the order of the Schur multiplier of a finite p-group given by Wiegold in 1969. The new bound is applied to the problem of classifying p-groups according to the size of their Schur multipliers.

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5

Onneweer, C. W., and T. S. Quek. "Multipliers for Hardy spaces on locally compact Vilenkin groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 55, no. 3 (December 1993): 287–301. http://dx.doi.org/10.1017/s1446788700034042.

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AbstractIn a recent paper In a recent paper the authors proved a multiplier theorem for Hardy spaces Hp (G), 0 < p ≤ 1, defined on a locally compact Vilenkin group G. The assumptions on the multiplier were expressed in terms of the “norms” of certain Herz spaces K (1/p − 1/?r, r, p) with r restricted to 1 ≤ r < ∞ and p < r. In the present paper we show how this restriction on r may be weakened to p ≤ r ∞. Furthermore, we present two modifications of our main theorem and compare these with certain results for multipliers on LP (Rn)-spaces, 1 < p < ∞, due to Seeger and to Cowling, Fendler and Foumier. We also discuss the sharpness of some of our results.

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6

Bloom, Walter R., and Zengfu Xu. "Fourier Multipliers For Local Hardy Spaces On Chébli-Trimèche Hypergroups." Canadian Journal of Mathematics 50, no. 5 (October 1, 1998): 897–928. http://dx.doi.org/10.4153/cjm-1998-047-9.

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AbstractIn this paper we consider Fourier multipliers on local Hardy spaces hp (0 < p ≤ 1) for Chébli-Trimèche hypergroups. The molecular characterization is investigated which allows us to prove a version of Hörmander’s multiplier theorem.

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7

Mostafa, Yasser E., and M. Hesham El Naggar. "Dynamic analysis of laterally loaded pile groups in sand and clay." Canadian Geotechnical Journal 39, no. 6 (December 1, 2002): 1358–83. http://dx.doi.org/10.1139/t02-102.

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Pile foundations supporting bridge piers, offshore platforms, and marine structures are required to resist not only static loading but also lateral dynamic loading. The static py curves are widely used to relate pile deflections to nonlinear soil reactions. The p-multiplier concept is used to account for the group effect by relating the load transfer curves of a pile in a group to the load transfer curves of a single pile. Some studies have examined the validity of the p-multiplier concept for the static and cyclic loading cases. However, the concept of the p-multiplier has not yet been considered for the dynamic loading case, and hence it is undertaken in the current study. An analysis of the dynamic lateral response of pile groups is described. The proposed analysis incorporates the static py curve approach and the plane strain assumptions to represent the soil reactions within the framework of a Winkler model. The model accounts for the nonlinear behaviour of the soil, the energy dissipation through the soil, and the pile group effect. The model was validated by analyzing the response of pile groups subjected to lateral Statnamic loading and comparing the results with field measured values. An intensive parametric study was performed employing the proposed analysis, and the results were used to establish dynamic soil reactions for single piles and pile groups for different types of sand and clay under harmonic loading with varying frequencies applied at the pile head. "Dynamic" p-multipliers were established to relate the dynamic load transfer curves of a pile in a group to the dynamic load transfer curves for a single pile. The dynamic p-multipliers were found to vary with the spacing between piles, soil type, peak amplitude of loading, and the angle between the line connecting any two piles and the direction of loading. The study indicated the effect of pile material and geometry, pile installation method, and pile head conditions on the p-multipliers. The calculated p-multipliers compared well with p-multipliers back-calculated from full scale field tests.Key words: lateral, transient loading, nonlinear, pilesoilpile interaction, py curves, Statnamic.

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8

Fraser, A. J. "An (n + 1)– fold Marcinkiewicz multiplier theorem on the Heisenberg group." Bulletin of the Australian Mathematical Society 63, no. 1 (February 2001): 35–58. http://dx.doi.org/10.1017/s0004972700019092.

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We prove a Marcinkiewicz-type multiplier theorem on the Heisenberg group: for 1 < p < ∞, we establish the boundedness on Lp (ℍn) of spectral multipliers m (ℒ1,…,ℒn, iT) of the n partial sub-Laplacians ℒ1,…,ℒn and iT, where m satisfies an (n + l)-fold Marcinkiewicz-type condition. We also establish regularity and cancellation conditions which the convolution kernels of these Marcinkiewicz multipliers m (ℒ1,…,ℒn,iT) satisfy.

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9

Hare, Kathryn E., and Enji Sato. "Spaces of Lorentz Multipliers." Canadian Journal of Mathematics 53, no. 3 (June 1, 2001): 565–91. http://dx.doi.org/10.4153/cjm-2001-024-5.

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AbstractWe study when the spaces of Lorentz multipliers from Lp,t → Lp,s are distinct. Our main interest is the case when s < t, the Lorentz-improving multipliers. We prove, for example, that the space of multipliers which map Lp,t → Lp,s is different from those mapping Lp,t → Lp,s if either r = p or p′ and 1/s − 1/t ≠ 1/u − 1/v, or r ≠ p or p′. These results are obtained by making careful estimates of the Lorentz multiplier norms of certain linear combinations of Fejer or Dirichlet kernels. For the case when the first indices are different the linear combination we analyze is in the spirit of a Rudin-Shapiro polynomial.

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10

Weigel, Th, and P. A. Zalesskiĭ. "Groups with infinite mod-p Schur multiplier." Journal of Algebra 344, no. 1 (October 2011): 70–77. http://dx.doi.org/10.1016/j.jalgebra.2011.06.033.

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11

Niroomand, Peyman, Farangis Johari, and Mohsen Parvizi. "c-Nilpotent Multiplier of Finite p-Groups." Bulletin of the Malaysian Mathematical Sciences Society 43, no. 1 (January 13, 2019): 941–56. http://dx.doi.org/10.1007/s40840-019-00723-x.

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12

FernÁndez-Alcober, Gustavo A., and Urban Jezernik. "BOGOMOLOV MULTIPLIERS OF P-GROUPS OF MAXIMAL CLASS." Quarterly Journal of Mathematics 71, no. 1 (December 6, 2019): 123–38. http://dx.doi.org/10.1093/qmathj/haz046.

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Abstract Let $G$ be a $p$-group of maximal class and order $p^n$. We determine whether or not the Bogomolov multiplier ${\operatorname{B}}_0(G)$ is trivial in terms of the lower central series of $G$ and $P_1 = C_G(\gamma _2(G) / \gamma _4(G))$. If in addition $G$ has positive degree of commutativity and $P_1$ is metabelian, we show how understanding ${\operatorname{B}}_0(G)$ reduces to the simpler commutator structure of $P_1$. This result covers all $p$-groups of maximal class of large-enough order, and, furthermore, it allows us to give the first natural family of $p$-groups containing an abundance of groups with non-trivial Bogomolov multipliers. We also provide more general results on Bogomolov multipliers of $p$-groups of arbitrary coclass $r$.

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13

Albrecht, Ernst, and Werner J. Ricker. "Functional calculi and decomposability of unbounded multiplier operators in LP(ℝN)." Proceedings of the Edinburgh Mathematical Society 38, no. 1 (February 1995): 151–66. http://dx.doi.org/10.1017/s0013091500006271.

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It is known, for each 1<p<∞, p≠2, that there exist differential operators in LP(ℝN) which are not (unbounded) decomposable operators in the sense of C. Foiaş. In this note we exhibit large classes of differential (and unbounded multiplier operators which are decomposable in LP(ℝN) and hence have good spectral mapping properties; the arguments are based on the existence of a sufficiently rich functional calculus. The basic idea is to take advantage of existing classical results on p-multipliers and use them to generate appropriate functional calculi.

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14

Daly, J. E., and S. Fridli. "Trigonometric Multipliers on H2π." Canadian Mathematical Bulletin 48, no. 3 (September 1, 2005): 370–81. http://dx.doi.org/10.4153/cmb-2005-034-5.

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AbstractIn this paper we consider multipliers on the real Hardy space H2π. It is known that the Marcinkiewicz and the Hörmander–Mihlin conditions are sufficient for the corresponding trigonometric multiplier to be bounded on , 1 < p < ∞. We show among others that the Hörmander– Mihlin condition extends to H2π but the Marcinkiewicz condition does not.

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15

Al-Saidy, Saheb K., Naseif J. AL-Jawari, and Ali Hussein Zaboon. "Best multiplier Approximation in L_(p,∅_n ) (B)." Al-Mustansiriyah Journal of Science 30, no. 2 (September 30, 2019): 27. http://dx.doi.org/10.23851/mjs.v30i2.541.

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The purpose of this paper is to find best multiplier approximation of unbounded functions in L_(p,∅_n ) –space by using Trigonometric polynomials and by de la Vallee- Poussin operators. Also we will estimate the degree of the best multiplier approximation by Weighted –Ditzian-Totik modulus

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16

Nemtseva, Yulia V., and Yulia V. Vorozhbickaya. "Methodological aspects of evaluating a company’s investment attractiveness." RUDN Journal of Economics 29, no. 1 (December 15, 2021): 114–25. http://dx.doi.org/10.22363/2313-2329-2021-29-1-114-125.

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The actual problems of choosing tools for risk assessment and predicted profitability (attractiveness) of an investment object are studied. There is a close relationship between the financial multipliers DIV/FCF, P/E Shiller, EV/EBITDA and risk indicators, which gives the investor the opportunity to make additional operational forecasts when analyzing an investment project. A number of key financial multipliers (P/S, EV/S, P/OCF, P/FCF) have been identified, and it is not entirely correct to use them as criteria for making an investment decision. The expediency of using the EV/EBITDA multiplier for making forecasts about the volatility of the return on shares of a certain company is justified, since this is the only indicator among the financial multipliers selected for analysis that has a relationship with the beta coefficient. Recommendations for forming a sample of necessary indicators (multipliers) when making investment decisions by various stakeholders are proposed.

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17

Adeel, Muhammad Bilal, Muhammad Asad Jan, Muhammad Aaqib, and Duhee Park. "Development of Simulation Based p-Multipliers for Laterally Loaded Pile Groups in Granular Soil Using 3D Nonlinear Finite Element Model." Applied Sciences 11, no. 1 (December 22, 2020): 26. http://dx.doi.org/10.3390/app11010026.

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The behavior of laterally loaded pile groups is usually accessed by beam-on-nonlinear-Winkler-foundation (BNWF) approach employing various forms of empirically derived p-y curves and p-multipliers. Averaged p-multiplier for a particular pile group is termed as the group effect parameter. In practice, the p-y curve presented by the American Petroleum Institute (API) is most often utilized for piles in granular soils, although its shortcomings are recognized. In this study, we performed 3D finite element analysis to develop p-multipliers and group effect parameters for 3 × 3 to 5 × 5 vertically squared pile groups. The effect of the ratio of spacing to pile diameter (S/D), number of group piles, varying friction angle (φ), and pile fixity conditions on p-multipliers and group effect parameters are evaluated and quantified. Based on the simulation outcomes, a new functional form to calculate p-multipliers is proposed for pile groups. Extensive comparisons with the experimental measurements reveal that the calculated p-multipliers and group effect parameters are within the recorded range. Comparisons with two design guidelines which do not account for the pile fixity condition demonstrate that they overestimate the p-multipliers for fixed-head condition.

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18

SZAREK, TOMASZ Z. "MULTIPLIERS OF LAPLACE TRANSFORM TYPE IN CERTAIN DUNKL AND LAGUERRE SETTINGS." Bulletin of the Australian Mathematical Society 85, no. 2 (December 15, 2011): 177–90. http://dx.doi.org/10.1017/s0004972711003078.

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AbstractWe investigate Laplace type and Laplace–Stieltjes type multipliers in the d-dimensional setting of the Dunkl harmonic oscillator with the associated group of reflections isomorphic to ℤd2 and in the related context of Laguerre function expansions of convolution type. We use Calderón–Zygmund theory to prove that these multiplier operators are bounded on weighted Lp, 1<p<∞, and from L1 to weak L1.

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19

Savas, E., A. F. Tenca, M. E. Ciftcibasi, and C. K. Koc. "Multiplier architectures for GF(p) and GF(2n)." IEE Proceedings - Computers and Digital Techniques 151, no. 2 (2004): 147. http://dx.doi.org/10.1049/ip-cdt:20040047.

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20

Rai, Pradeep K. "On the Schur multiplier of special p -groups." Journal of Pure and Applied Algebra 222, no. 2 (February 2018): 316–22. http://dx.doi.org/10.1016/j.jpaa.2017.04.004.

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21

WEI, SHUGANG, and KENSUKE SHIMIZU. "MODULO (2p ± 1) MULTIPLIERS USING A THREE-OPERAND MODULAR SIGNED-DIGIT ADDITION ALGORITHM." Journal of Circuits, Systems and Computers 15, no. 01 (February 2006): 129–44. http://dx.doi.org/10.1142/s0218126606002976.

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In this paper, a new three-operand modulo (2p ± 1) addition is implemented by performing a carry-save addition and a two-operand modular addition based on the p-digit radix-two signed-digit (SD) number system. Thus, the delay time of the three-operand modular adder is independent of the word length of the operands. A modulo (2p ± 1) multiplier is constructed as a ternary tree of the three-operand modular SD adders, and the modular multiplication time is proportional to log 3 p. When a serial modular multiplier is constructed using the three-operand modular SD adder, two modular partial products can be added to the sum at the same time. Two kinds of Booth recoding methods are also proposed to reduce the partial products from p to p/2. Therefore, the performance of a parallel modular multiplier can be modified by reducing half of the modular SD adders in the adder tree. For a serial modular multiplication, two partial products are generated from two Booth recoders and added to the sum by using one three-operand modular SD adder, so that the speed of the modular multiplication is three times as fast as the speed without using the three-operand modular SD adder and the Booth recoding method. A very large-scale integration (VLSI) implementation method by VHDL is also discussed. The design and simulation results show that high-speed modular multipliers can be obtained by the algorithms presented.

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22

Garrigós, Gustavo, and Andreas Seeger. "On plate decompositions of cone multipliers." Proceedings of the Edinburgh Mathematical Society 52, no. 3 (September 23, 2009): 631–51. http://dx.doi.org/10.1017/s001309150700048x.

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AbstractAn important inequality due to Wolff on plate decompositions of cone multipliers is known to have consequences for sharp Lp results on cone multipliers, local smoothing for the wave equation, convolutions with radial kernels, Bergman projections in tubes over cones, averages over finite-type curves in ℝ3 and associated maximal functions. We observe that the range of p in Wolff's inequality, for the conic and the spherical versions, can be improved by using bilinear restriction results. We also use this inequality to give some improved estimates on square functions associated to decompositions of cone multipliers in low dimensions. This gives a new L4 bound for the cone multiplier operator in ℝ3.

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23

Brown, Lawrence G. "Close hereditary C*-subalgebras and the structure of quasi-multipliers." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 2 (January 16, 2017): 263–92. http://dx.doi.org/10.1017/s0308210516000172.

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We answer a question of Takesaki by showing that the following can be derived from the thesis of Shen: if A and B are σ-unital hereditary C*-subalgebras of C such that ‖p – q‖ < 1, where p and q are the corresponding open projections, then A and B are isomorphic. We give some further elaborations and counterexamples with regard to the σ-unitality hypothesis. We produce a natural one-to-one correspondence between complete order isomorphisms of C*-algebras and invertible left multipliers of imprimitivity bimodules. A corollary of the above two results is that any complete order isomorphism between σ-unital C*-algebras is the composite of an isomorphism with an inner complete order isomorphism. We give a separable counterexample to a question of Akemann and Pedersen; namely, the space of quasi-multipliers is not linearly generated by left and right multipliers. But we show that the space of quasi-multipliers is multiplicatively generated by left and right multipliers in the σ-unital case. In particular, every positive quasi-multiplier is of the form T*T for T a left multiplier. We show that a Lie theory consequence of the negative result just stated is that the map sending T to T*T need not be open, even for very nice C*-algebras. We show that surjective maps between σ-unital C*-algebras induce surjective maps on left, right, and quasi-multipliers. (The more significant similar result for multipliers is Pedersen's non-commutative Tietze extension theorem.) We elaborate the relations of the above with continuous fields of Hilbert spaces and in so doing answer a question of Dixmier and Douady. We discuss the relationship of our results to the theory of perturbations of C*-algebras.

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24

Urowitz, Murray B., Dominique Ibañez, Jiandong Su, and Dafna D. Gladman. "Modified Framingham Risk Factor Score for Systemic Lupus Erythematosus." Journal of Rheumatology 43, no. 5 (February 15, 2016): 875–79. http://dx.doi.org/10.3899/jrheum.150983.

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Objective.The traditional Framingham Risk Factor Score (FRS) underestimates the risk for coronary artery disease (CAD) in patients with systemic lupus erythematosus (SLE). We aimed to determine whether an adjustment to the FRS would more accurately reflect the higher prevalence of CAD among patients with SLE.Methods.Patients with SLE without a previous history of CAD or diabetes followed regularly at the University of Toronto Lupus Clinic were included. A modified FRS (mFRS) was calculated by multiplying the items by 1.5, 2, 3, or 4. In the first part of the study, using one-third of all eligible patients, we evaluated the sensitivity and specificity of the FRS and the different multipliers for the mFRS. In the second part of the study, using the remaining 2/3 of the eligible patients, we compared the predictive ability of the FRS to the mFRS. In the third part of the study, we assessed the prediction for CAD in a time-dependent analysis of the FRS and mFRS.Results.There were 905 women (89.3%) with a total of 95 CAD events included. In part 1, we determined that a multiplier of 2 provided the best combination of sensitivity and specificity. In part 2, 2.4% of the patients were classified as moderate/high risk based on the classic FRS and 17.3% using the 2FRS (the FRS with a multiplier of 2). In part 3, a time-dependent covariate analysis for the prediction of the first CAD event revealed an HR of 3.22 (p = 0.07) for the classic FRS and 4.37 (p < 0.0001) for the 2FRS.Conclusion.An mFRS in which each item is multiplied by 2 more accurately predicts CAD in patients with SLE.

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25

Blower, G. "Multipliers for semigroups." Proceedings of the Edinburgh Mathematical Society 39, no. 2 (June 1996): 241–52. http://dx.doi.org/10.1017/s0013091500022975.

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Let L be a positive invertible self-adjoint operator in L2(X;C). Using transference methods for locally bounded groups of operators we obtain multipliers for the group of complex powers Liu on vector-valued Lebesgue spaces. Using a Mellin inversion formula, we derive a sufficient condition for a function to be a multiplier of the semigroup e-tL on Lp(X;E) where E is a UMD Banach space and 1<p<∞.

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26

Wang, Li-an Daniel. "A Multiplier Theorem on Anisotropic Hardy Spaces." Canadian Mathematical Bulletin 61, no. 2 (June 1, 2018): 390–404. http://dx.doi.org/10.4153/cmb-2017-029-0.

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AbstractWe present a multiplier theorem on anisotropic Hardy spaces. When m satisfies the anisotropic, pointwise Mihlin condition, we obtain boundedness of the multiplier operator Tm: → , for the range of p that depends on the eccentricities of the dilation A and the level of regularity of a multiplier symbol m. This extends the classical multiplier theorem of Taibleson andWeiss.

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27

Ricker, Werner J., and Luis Rodríguez-Piazza. "Absolutely summing multiplier operators in $L^p (G)$ for $p > 2$." Proceedings of the American Mathematical Society 142, no. 12 (August 18, 2014): 4305–13. http://dx.doi.org/10.1090/s0002-9939-2014-12179-4.

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28

MOHAMMADZADEH, FAHIMEH, AZAM HOKMABADI, and BEHROOZ MASHAYEKHY. "ON THE EXPONENT OF THE SCHUR MULTIPLIER OF A PAIR OF FINITE p-GROUPS." Journal of Algebra and Its Applications 12, no. 08 (July 31, 2013): 1350053. http://dx.doi.org/10.1142/s0219498813500539.

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In this paper, we find an upper bound for the exponent of the Schur multiplier of a pair (G, N) of finite p-groups, when N admits a complement in G. As a consequence, we show that the exponent of the Schur multiplier of a pair (G, N) divides exp (N) if (G, N) is a pair of finite p-groups of class at most p – 1. We also prove that if N is powerfully embedded in G, then the exponent of the Schur multiplier of a pair (G, N) divides exp (N).

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29

NIROOMAND, PEYMAN, and MOHSEN PARVIZI. "ON THE 2-NILPOTENT MULTIPLIER OF FINITE p-GROUPS." Glasgow Mathematical Journal 57, no. 1 (December 22, 2014): 201–10. http://dx.doi.org/10.1017/s0017089514000263.

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AbstractThe purpose of this paper is a further investigation on the 2-nilpotent multiplier, $\mathcal{M}$(2)(G), when G is a non-abelian p-group. Furthermore, taking G in the class of extra-special p-groups, we will get the explicit structure of $\mathcal{M}$(2)(G) and will classify 2-capable groups in that class.

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30

Trujillo-Olaya, Vladimir, and Jaime Velasco-Medina. "Half-Matrix Normal Basis Multiplier Over GF( $p^{m}$ )." IEEE Transactions on Circuits and Systems I: Regular Papers 64, no. 4 (April 2017): 879–91. http://dx.doi.org/10.1109/tcsi.2016.2626375.

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31

Ashour, Mohamed, and Hamed Ardalan. "Employment of the P-Multiplier in Pile-Group Analysis." Journal of Bridge Engineering 16, no. 5 (September 2011): 612–23. http://dx.doi.org/10.1061/(asce)be.1943-5592.0000196.

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32

Zlobec, S. "Constrained Optimization and Lagrange Multiplier Rules (Dimitri P. Bertsekas)." SIAM Review 27, no. 1 (March 1985): 131–32. http://dx.doi.org/10.1137/1027051.

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33

LIN, CHIN-CHENG. "HÖRMANDER'S $H^p$ MULTIPLIER THEOREM FOR THE HEISENBERG GROUP." Journal of the London Mathematical Society 67, no. 03 (May 20, 2003): 686–700. http://dx.doi.org/10.1112/s0024610703004150.

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34

Hatui, Sumana. "Finite p -groups having Schur multiplier of maximum order." Journal of Algebra 492 (December 2017): 490–97. http://dx.doi.org/10.1016/j.jalgebra.2017.09.013.

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35

Mockenhaupt, Gerd, and Werner J. Ricker. "Approximation of p-multiplier Operators via their Spectral Projections." Positivity 12, no. 1 (October 29, 2007): 133–50. http://dx.doi.org/10.1007/s11117-007-2139-x.

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36

Mustaţă, Mircea, and Ken-Ichi Yoshida. "Test Ideals Vs. Multiplier Ideals." Nagoya Mathematical Journal 193 (2009): 111–28. http://dx.doi.org/10.1017/s0027763000026052.

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AbstractThe generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via vanishing theorems. In this note we give several examples to emphasize the different behavior of test ideals and multiplier ideals. Our main result is that every ideal in an F-finite regular local ring can be written as a generalized test ideal. We also prove the semicontinuity of F-pure thresholds (though the analogue of the Generic Restriction Theorem for multiplier ideals does not hold).

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37

Awaludin, Asep Muhamad, Harashta Tatimma Larasati, and Howon Kim. "High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA." Sensors 21, no. 4 (February 19, 2021): 1451. http://dx.doi.org/10.3390/s21041451.

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In this paper, we present a high-speed, unified elliptic curve cryptography (ECC) processor for arbitrary Weierstrass curves over GF(p), which to the best of our knowledge, outperforms other similar works in terms of execution time. Our approach employs the combination of the schoolbook long and Karatsuba multiplication algorithm for the elliptic curve point multiplication (ECPM) to achieve better parallelization while retaining low complexity. In the hardware implementation, the substantial gain in speed is also contributed by our n-bit pipelined Montgomery Modular Multiplier (pMMM), which is constructed from our n-bit pipelined multiplier-accumulators that utilizes digital signal processor (DSP) primitives as digit multipliers. Additionally, we also introduce our unified, pipelined modular adder/subtractor (pMAS) for the underlying field arithmetic, and leverage a more efficient yet compact scheduling of the Montgomery ladder algorithm. The implementation for 256-bit modulus size on the 7-series FPGA: Virtex-7, Kintex-7, and XC7Z020 yields 0.139, 0.138, and 0.206 ms of execution time, respectively. Furthermore, since our pMMM module is generic for any curve in Weierstrass form, we support multi-curve parameters, resulting in a unified ECC architecture. Lastly, our method also works in constant time, making it suitable for applications requiring high speed and SCA-resistant characteristics.

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38

Rhodes, John A. "The theta multiplier for number fields via p-adic planes." Pacific Journal of Mathematics 177, no. 1 (January 1, 1997): 161–86. http://dx.doi.org/10.2140/pjm.1997.177.161.

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39

Berkson, Earl, T. Gillespie, and Paul Muhly. "$L^{p}$-Multiplier transference induced by representations in Hilbert space." Studia Mathematica 94, no. 1 (1989): 51–61. http://dx.doi.org/10.4064/sm-94-1-51-61.

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40

Niroomand, Peyman. "The Schur multiplier of p-groups with large derived subgroup." Archiv der Mathematik 95, no. 2 (July 8, 2010): 101–3. http://dx.doi.org/10.1007/s00013-010-0154-9.

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41

Giles, Jane, and Patrick Phillips. "P-172 Multiplier effects: a model for health professional development." Diabetes Research and Clinical Practice 79 (February 2008): S117—S118. http://dx.doi.org/10.1016/s0168-8227(08)70940-9.

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42

Mockenhaupt, G., S. Okada, and W. J. Ricker. "Optimal Extension of Fourier Multiplier Operators in L p (G)." Integral Equations and Operator Theory 68, no. 4 (September 23, 2010): 573–99. http://dx.doi.org/10.1007/s00020-010-1829-0.

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43

Chiou, C. W., J. M. Lin, and C. Y. Lee. "Unified dual-field multiplier in GF(P) and GF(2k)." IET Information Security 3, no. 2 (June 1, 2009): 45–52. http://dx.doi.org/10.1049/iet-ifs.2007.0030.

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44

Bhavani, M., M. Siva Kumar, and K. Srinivas Rao. "Delay Comparison for 16x16 Vedic Multiplier Using RCA and CLA." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 3 (June 1, 2016): 1205. http://dx.doi.org/10.11591/ijece.v6i3.9457.

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<p>In any integrated chip compulsory adders are required because first they are fast and second are the less power consumption and delay. And at the same time multiplication process is also used in various applications. So as the speed of multiplier increases then the speed of processor also increases. And hence we are proposing the Vedic multiplier using these adders. Vedic multiplier is an ancient mathematics which uses mainly 16 sutras for its operation. In this project we are using “urdhva triyagbhyam” sutra to do our process. This paper proposes the Vedic multiplier using the adders ripple carry adder(RCA) and carry look ahead adder(CLA) and puts forward that CLA is better than RCA.The major parameters we are simulating here are number of slices and delay. The code is written by using Verilog and is implemented using Xilinx ISE Design Suite.</p>

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45

Bhavani, M., M. Siva Kumar, and K. Srinivas Rao. "Delay Comparison for 16x16 Vedic Multiplier Using RCA and CLA." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 3 (June 1, 2016): 1205. http://dx.doi.org/10.11591/ijece.v6i3.pp1205-1212.

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<p>In any integrated chip compulsory adders are required because first they are fast and second are the less power consumption and delay. And at the same time multiplication process is also used in various applications. So as the speed of multiplier increases then the speed of processor also increases. And hence we are proposing the Vedic multiplier using these adders. Vedic multiplier is an ancient mathematics which uses mainly 16 sutras for its operation. In this project we are using “urdhva triyagbhyam” sutra to do our process. This paper proposes the Vedic multiplier using the adders ripple carry adder(RCA) and carry look ahead adder(CLA) and puts forward that CLA is better than RCA.The major parameters we are simulating here are number of slices and delay. The code is written by using Verilog and is implemented using Xilinx ISE Design Suite.</p>

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46

Hatui, Sumana. "Schur multipliers of special 𝑝-groups of rank 2." Journal of Group Theory 23, no. 1 (January 1, 2020): 85–95. http://dx.doi.org/10.1515/jgth-2019-0045.

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AbstractLet G be a special p-group with center of order {p^{2}}. Berkovich and Janko asked to find the Schur multiplier of G in [Y. Berkovich and Z. Janko, Groups of Prime Power Order. Volume 3, De Gruyter Exp. Math. 56, Walter de Gruyter, Berlin, 2011; Problem 2027]. In this article, we answer this question by explicitly computing the Schur multiplier of these groups.

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Schinianakis, D. M., A. P. Fournaris, H. E. Michail, A. P. Kakarountas, and T. Stouraitis. "An RNS Implementation of an $F_{p}$ Elliptic Curve Point Multiplier." IEEE Transactions on Circuits and Systems I: Regular Papers 56, no. 6 (June 2009): 1202–13. http://dx.doi.org/10.1109/tcsi.2008.2008507.

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48

Johnson, Michael S., Joshua L. Beutler, Alan P. Nelson, and Aaron R. Hawkins. "Solid-State Impact-Ionization Multiplier With P-N Junction Injection Node." IEEE Transactions on Electron Devices 56, no. 6 (June 2009): 1360–64. http://dx.doi.org/10.1109/ted.2009.2019421.

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49

Niroomand, Peyman. "On the order of Schur multiplier of non-abelian p-groups." Journal of Algebra 322, no. 12 (December 2009): 4479–82. http://dx.doi.org/10.1016/j.jalgebra.2009.09.030.

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50

Sharma, Mahendra, and Santhosh Kumar Singh. "New Technique Based Peasant Multiplication for Effcient Signal Processing Applications." Indonesian Journal of Electrical Engineering and Computer Science 8, no. 3 (December 1, 2017): 726. http://dx.doi.org/10.11591/ijeecs.v8.i3.pp726-729.

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<p class="Standard"><span lang="EN-IN">The Direct Form FIR channel is utilized for DSP application where the channel request is settled. For the most part this channel devours more range and power. To defeat this issue Multiplier Control Signal Decision window (MCSD) plans is joined into Direct Form FIR channel to powerfully change the channel arrange. MCSD structures comprise of Control flag Generator (CG) and Amplitude Detection (AD) rationale circuits. Advertisement rationale is utilized to disavow the correct duplication process and screen the amplitudes of information tests. CG is utilized to control the channel operation through inside counter. Traditional reconfigurable FIR channel is planned utilizing Vedic Multiplier that devours more territory and deferral. In this paper, changed reconfigurable FIR filer is intended to additionally decrease the APT (Area, Power and Timing) item. The proposed Reconfigurable FIR filer, Vedic Multiplier is supplanted by Russian Peasant Multiplication procedure. Subsequently adjusted Reconfigurable FIR channel with Russian Peasant Multiplier expends less region, postponement and power than all analyzed techniques.</span></p>

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