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Manoj Sharma - One of the best experts on this subject based on the ideXlab platform.
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a note on a generalized m series as a Special Function of fractional calculus
2009Co-Authors: Manoj Sharma, Renu JainAbstract:In this note we like to bring audience’ attention to a further extension of both Mittag-Le†er Function and generalized hypergeometric Function pFq, called generalized M-series. This is a continuation of our previous note [10] and an interesting example of the Special Functions of Fractional Calculus (SF of FC), in the sense of [7] and [2],[3], a notion that gained recently an important role in the theory of difierentiation of arbitrary order and in the solutions of fractional order difierential equations. We give representations of the generalized M-series in terms of the Wright generalized hypergeometric Function p“q and Fox’s H-Function, and formulas for fractional calculus operators of it. Mathematics Subject Classiflcation: 26A33, 33C60, 44A15
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fractional integration and fractional differentiation of the m series
Fractional Calculus and Applied Analysis, 2008Co-Authors: Manoj SharmaAbstract:In this paper a new Special Function called as M-series is introduced. This series is a particular case of the H-Function of Inayat-Hussain. The M-series is interesting because the pFq-hypergeometric Function and the Mittag-Leffler Function follow as its particular cases, and these Functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note that the MittagLeffler Function occurs as solution of fractional integral equations in those area. In this short note we have obtained formulas for the fractional integral and fractional derivative of the M-series. Mathematics Subject Classification: 26A33, 33C60, 44A15
Enrico Masina - One of the best experts on this subject based on the ideXlab platform.
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erratum on modifications of the exponential integral with the mittag leffler Function
Fractional Calculus and Applied Analysis, 2018Co-Authors: Francesco Mainardi, Enrico MasinaAbstract:In this paper we survey the properties of the Schelkunoff modification of the Exponential integral and we generalize it with the Mittag-Leffler Function. So doing we get a new Special Function (as far as we know) that may be relevant in linear viscoelasticity because of its complete monotonicity properties in the time domain. We also consider the generalized sine and cosine integral Functions
Leesup Kim - One of the best experts on this subject based on the ideXlab platform.
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MRTP: Mobile Ray Tracing Processor With Reconfigurable Stream Multi-Processors for High Datapath Utilization
IEEE Journal of Solid-State Circuits, 2012Co-Authors: Hongyun Kim, Youngjun Kim, Leesup KimAbstract:This paper presents a mobile ray tracing processor (MRTP) with reconfigurable stream multi-processors (RSMPs) for high datapath utilization. The MRTP includes three RSMPs that operate in multiple instruction multiple data (MIMD) mode asynchronously to exploit instruction-level parallelism. Each RSMP is based on single instruction multiple thread (SIMT) architecture to exploit thread-level parallelism. An RSMP consists of twelve scalar processing elements (SPEs) that run multiple threads in parallel synchronously: twelve scalar threads or four vector threads depending on an operating mode. A low datapath utilization caused by a branch divergence in SIMT architecture is improved by 19.9% on average by reconfiguring twelve SPEs between scalar SIMT and vector SIMT with 0.1% area overheads. Special Function instructions occupy only 2% ~ 8% of kernel instructions so that a partial Special Function unit (PSFU) is implemented instead of a large dedicated SFU. The access conflicts with a look-up table (LUT) caused by concurrent accesses of twelve SPEs are reduced by a table loader (TBLD). The TBLD monitors concurrent requests from twelve SPEs and reduces an access count to LUT by distributing a coefficient to multiple SPEs with only one read-access to LUT. MRTP with area of 4 × 4 mm2 has been fabricated in 0.13 μm CMOS technology. MRTP achieves a peak performance of 673 K rays per second while consuming 156 mW at 100 MHz with VDD = 1.2 V .
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area efficient Special Function unit for mobile vertex processors
Electronics Letters, 2009Co-Authors: Kyusik Chung, Leesup KimAbstract:An area-efficient Special Function unit (SFU) for the evaluation of transcendental Functions in mobile vertex processors is presented. In spite of infrequent usage, previous implementation of an SFU occupied significant portion of a shader datapath unit. The proposed SFU reduces the area by 54% by performing quadratic interpolation included in the Function evaluation with a shared 4D dot product unit and implementing setup circuitry and a lookup table by dedicated hardware for the SFU. By benchmarking shader programs, the performance/area of a shader datapath unit turns out to be improved by 69%.
Mark W. Coffey - One of the best experts on this subject based on the ideXlab platform.
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Mellin transforms with only critical zeros: Legendre Functions
Journal of Number Theory, 2015Co-Authors: Mark W. Coffey, Matthew C. LettingtonAbstract:We consider the Mellin transforms of certain Legendre Functions based upon the ordinary and associated Legendre polynomials. We show that the transforms have polynomial factors whose zeros lie all on the critical line View the MathML sourceRes=1/2. The polynomials with zeros only on the critical line are identified in terms of certain View the MathML sourceF23(1) hypergeometric Functions. These polynomials possess the Functional equation pn(s)=(−1)⌊n/2⌋pn(1−s)pn(s)=(−1)⌊n/2⌋pn(1−s). Other hypergeometric representations are presented, as well as certain Mellin transforms of fractional part and fractional part-integer part Functions. The results should be of interest to Special Function theory, combinatorial geometry, and analytic number theory.
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mellin transforms with only critical zeros generalized hermite Functions
arXiv: Complex Variables, 2013Co-Authors: Mark W. CoffeyAbstract:We consider the Mellin transforms of certain generalized Hermite Functions based upon certain generalized Hermite polynomials, characterized by a parameter $\mu>-1/2$. We show that the transforms have polynomial factors whose zeros lie all on the critical line. The polynomials with zeros only on the critical line are identified in terms of certain $_2F_1(2)$ hypergeometric Functions, being certain scaled and shifted Meixner-Pollaczek polynomials. Other results of Special Function theory are presented.
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Mellin transforms with only critical zeros: Legendre Functions
arXiv: Mathematical Physics, 2013Co-Authors: Mark W. Coffey, Matthew C. LettingtonAbstract:We consider the Mellin transforms of certain Legendre Functions based upon the ordinary and associated Legendre polynomials. We show that the transforms have polynomial factors whose zeros lie all on the critical line Re $s=1/2$. The polynomials with zeros only on the critical line are identified in terms of certain $_3F_2(1)$ hypergeometric Functions. These polynomials possess the Functional equation $p_n(s)=(-1)^{\lfloor n/2 \rfloor} p_n(1-s)$. Other hypergeometric representations are presented, as well as certain Mellin transforms of fractional part and fractional part-integer part Functions. The results should be of interest to Special Function theory, combinatorial geometry, and analytic number theory.
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mellin transforms with only critical zeros chebyshev and gegenbauer Functions
arXiv: Mathematical Physics, 2013Co-Authors: Mark W. Coffey, Matthew C. LettingtonAbstract:We consider the (generalized) Mellin transforms of certain Chebyshev Functions based upon the Chebyshev polynomials. We show that the transforms have polynomial factors whose zeros lie all on the critical line or on the real line. The polynomials with zeros only on the critical line are identified in terms of certain 3F2(1) hypergeometric Functions. Furthermore, we extend this result to a 1-parameter family of polynomials with zeros only on the critical line. These polynomials possess the Functional equation pn(s;�) = (−1) ⌊n/2⌋ pn(1 − s;�). We then present the generalization to the Mellin transform of certain Gegenbauer Functions. The results should be of interest to Special Function theory, combinatorics, and analytic number theory.
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a set of identities for a class of alternating binomial sums arising in computing applications
arXiv: Mathematical Physics, 2006Co-Authors: Mark W. CoffeyAbstract:We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and Special Function and Special number representations is used. The results are sufficiently general to subsume several previously known cases. Extensions of the method are apparent and are outlined.
Anatoly A Kilbas - One of the best experts on this subject based on the ideXlab platform.
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integral transform with the extended generalized mittag leffler Function
Mathematical Modelling and Analysis, 2006Co-Authors: Anatoly A Kilbas, A A KorolevaAbstract:Abstract The paper is devoted to the study of the integral transform containing the Special Function a((a, â) n ;z) generalizing the Mittag‐Leffler type Function in the space £v,r (1 ≤ r ≤ 8, i ∈ R) of Lebesgue measurable Functions on R+ = (0,+8) such that ‖ƒ‖ v,r < 8, where Mapping properties such as the boundedness, the range, the representation and the inversion of the considered transform are proved. The results are based on the representation of the considered transform as the H‐transform.
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fractional integrals and derivatives theory and applications
1993Co-Authors: Stefan Samko, Anatoly A Kilbas, Oleg Igorevich MarichevAbstract:Fractional integrals and derivatives on an interval fractional integrals and derivatives on the real axis and half-axis further properties of fractional integrals and derivatives other forms of fractional integrals and derivatives fractional integrodifferentiation of Functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations fo the first kind with Special Function kernels applications to differential equations.
