scholarly journals Refinements of Gaussian Tail Inequality

2018 ◽  
pp. 1-8
Author(s):  
N. A. Rather ◽  
T. A. Rather
Keyword(s):  
General Result ◽  
Normal Density ◽  
Special Cases ◽  
Tail Bound

In this paper, we first prove a theorem which gives considerably better bound for 0 ≤ t ≤ 1/2 than Gaussian tail inequality (or tail bound for normal density) and thus is a refinement of Gaussian tail inequality in this case. Next we present an interesting result which provides a refinement of Gaussian tail inequality for t > √ 3. Besides, we also prove an improvement of Gaussian tail inequality for 0 < t ≤ 1/2. Finally, we present a more general result which includes a variety of interesting results as special cases.

scholarly journals Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 250-252 ◽  
Author(s):  
Tobias Fritz
Keyword(s):  
Topological Space ◽  
General Result ◽  
Elementary Proof ◽  
Short Note ◽  
Stochastic Order ◽  
Topological Spaces ◽  
Probability Measures ◽  
Ordered Topological Space ◽  
Special Cases

Abstract In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.

Raman scattering from impurities in semiconductors. II. Special cases

1978 ◽  
Vol 56 (5) ◽  
pp. 560-564
Author(s):  
Robert Barrie ◽  
H. -C. Chow
Keyword(s):  
Raman Scattering ◽  
General Result ◽  
Phonon Scattering ◽  
Phonon Coupling ◽  
Strong Electron ◽  
Impurities In Semiconductors ◽  
Electron Phonon Coupling ◽  
Special Cases ◽  
Weak Electron

Special cases of the general result for Raman scattering from an impurity in a semiconductor are discussed. For weak electron–phonon coupling the zero-phonon and one-phonon scattering intensities are derived. For strong electron–phonon coupling a comparison is made between two different approximations that have been previously used.

Extension of normal functionals on W*-tensor products

1975 ◽  
Vol 78 (2) ◽  
pp. 301-307 ◽  
Author(s):  
Simon Wassermann
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Hilbert Spaces ◽  
General Result ◽  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann ◽  
Hilbert Algebras ◽  
Special Cases

A deep result in the theory of W*-tensor products, the Commutation theorem, states that if M and N are W*-algebras faithfully represented as von Neumann algebras on the Hilbert spaces H and K, respectively, then the commutant in L(H ⊗ K) of the W*-tensor product of M and N coincides with the W*-tensor product of M′ and N′. Although special cases of this theorem were established successively by Misonou (2) and Sakai (3), the validity of the general result remained conjectural until the advent of the Tomita-Takesaki theory of Modular Hilbert algebras (6). As formulated, the Commutation theorem is a spatial result; that is, the W*-algebras in its statement are taken to act on specific Hilbert spaces. Not surprisingly, therefore, known proofs rely heavily on techniques of representation theory.

scholarly journals Optimal Strategy for the Vardi Casino with Interest Payments

2007 ◽  
Vol 44 (01) ◽  
pp. 199-211 ◽  
Author(s):  
Ilie Grigorescu ◽  
Robert Chen ◽  
Larry Shepp
Keyword(s):  
General Result ◽  
Optimal Strategy ◽  
Critical Value ◽  
Discount Factor ◽  
Optimal Probability ◽  
Special Cases ◽  
Interest Payments

A gambler starts with fortune f &lt; 1 and plays in a Vardi casino with infinitely many tables indexed by their odds, r ≥ 0. In addition, all tables return the same expected winnings per dollar, c &lt; 0, and a discount factor is applied after each round. We determine the optimal probability of reaching fortune 1, as well as an optimal strategy that is different from bold play for fortunes larger than a critical value depending exclusively on c and 1 + a, the discount factor. The general result is computed explicitly for some relevant special cases. The question of whether bold play is an optimal strategy is discussed for various choices of the parameters.

Universal Hilbert subsets

1998 ◽  
Vol 124 (1) ◽  
pp. 127-134 ◽  
Author(s):  
PIERRE DÈBES ◽  
UMBERTO ZANNIER
Keyword(s):  
General Result ◽  
Special Cases

We show that the sequence 2n+n is a universal Hilbert sequence. That is, for each polynomial P(T, Y) irreducible in ℚ(T) [Y], the polynomial P(2n+n, Y) is irreducible in ℚ[Y] for all but finitely many n. This answers a question of M. Yasumoto. Other examples, like 2n+5n, are given. They are all obtained as special cases of a more general result which is proved from classical diophantine arguments.

scholarly journals MOCK THETA DOUBLE SUMS

2016 ◽  
Vol 59 (2) ◽  
pp. 323-348 ◽  
Author(s):  
JEREMY LOVEJOY ◽  
ROBERT OSBURN
Keyword(s):  
General Result ◽  
Theta Functions ◽  
Similar Type ◽  
Mock Theta Functions ◽  
Bailey Pairs ◽  
Special Cases ◽  
Seventh Order

AbstractWe prove a general result on Bailey pairs and show that two Bailey pairs of Bringmann and Kane are special cases. We also show how to use a change of base formula to pass from the pairs of Bringmann and Kane to pairs used by Andrews in his study of Ramanujan's seventh order mock theta functions. We derive several more Bailey pairs of a similar type and use these to construct a number of new q-hypergeometric double sums which are mock theta functions. Finally, we prove identities between some of these mock theta double sums and classical mock theta functions.

scholarly journals Cylindrical-wave diffraction by a rational wedge

1987 ◽  
Vol 411 (1841) ◽  
pp. 285-303 ◽  
Keyword(s):  
Half Plane ◽  
General Result ◽  
Wave Diffraction ◽  
Cylindrical Wave ◽  
Open Angle ◽  
Source Terms ◽  
Special Cases ◽  
Rational Multiple

In this paper, new expressions for the field produced by the diffraction of a cylindrical wave by a wedge, whose angle can be expressed as a rational multiple of π, are given. The solutions are expressed in terms of source terms and real integrals that represent the diffracted field. The general result obtained includes as special cases, Macdonald’s solution for diffraction by a half plane, a solution for Carslaw’s problem of diffraction by a wedge of open angle 2/3π, and a new representation for the solution of the problem of diffraction by a mixed soft-hard half plane.

Slender-body expressions for the wave load on offshore structures

1995 ◽  
Vol 450 (1939) ◽  
pp. 391-416 ◽  
Keyword(s):  
Cross Sections ◽  
General Result ◽  
Offshore Structures ◽  
Slender Body ◽  
Structural Members ◽  
Wave Load ◽  
Offshore Structure ◽  
Complete Structure ◽  
Special Cases ◽  
Surface Intersections

Expressions for the wave load on an offshore structure have recently been derived by several authors, by applying the classical slender-body approach to individual structural members. This paper shows that they are all special cases of a more general result, which covers a complete structure, including the effect of non-circular member cross-sections, joints between members, and surface intersections. This more general result cannot readily be derived by the methods adopted by the earlier authors; it relies on an energy argument.

scholarly journals Optimal Strategy for the Vardi Casino with Interest Payments

2007 ◽  
Vol 44 (1) ◽  
pp. 199-211 ◽  
Author(s):  
Ilie Grigorescu ◽  
Robert Chen ◽  
Larry Shepp
Keyword(s):  
General Result ◽  
Optimal Strategy ◽  
Critical Value ◽  
Discount Factor ◽  
Optimal Probability ◽  
Special Cases ◽  
Interest Payments

A gambler starts with fortune f < 1 and plays in a Vardi casino with infinitely many tables indexed by their odds, r ≥ 0. In addition, all tables return the same expected winnings per dollar, c < 0, and a discount factor is applied after each round. We determine the optimal probability of reaching fortune 1, as well as an optimal strategy that is different from bold play for fortunes larger than a critical value depending exclusively on c and 1 + a, the discount factor. The general result is computed explicitly for some relevant special cases. The question of whether bold play is an optimal strategy is discussed for various choices of the parameters.

scholarly journals Fixed point theorems for occasionally weakly compatible mappings, II

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 963-967 ◽  
Author(s):  
B.E. Rhoades
Keyword(s):  
Fixed Point ◽  
General Result ◽  
Fixed Point Theorems ◽  
Weakly Compatible Mappings ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Special Cases

In this paper we point out that a number of fixed point papers, involving several maps, are special cases of a general result proved several years ago by the author and G. F. Jungck, and one proved by Aliouche and Popa [1].

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