The Divisibility Modulo 4 of Kloosterman Sums over Finite Fields of Characteristic 3

Recently Garashuk and Lisonek evaluated Kloosterman sums K (a) modulo 4 over a finite field F3m in the case of even K (a). They posed it as an open problem to characterize elements a in F3m for which K (a) ≡ 1 (mod4) and K (a) ≡ 3 (mod4). In this paper, we will give an answer to this problem. The result allows us to count the number of elements a in F3m belonging to each of these two classes.

On the Exponential Bound of the Cutoff Resolvent

A simpler proof of a result of Burq [1] is presented.

Integer Points Close to a Smooth Curve

∗ This research is partially supported by the Bulgarian National Science Fund under contract MM-403/9

Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

Triples of Positive Integers with the same Sum and the same Product

It is proved that for every k there exist k triples of positive integers with the same sum and the same product.

Structural Analysis of Contours as the Sequences of the Digital Straight Segments and of the Digital Curve Arcs

Recognition of the object contours in the image as sequences of digital straight segments and/or digital curve arcs is considered in this article. The definitions of digital straight segments and of digital curve arcs are proposed. The methods and programs to recognize the object contours are represented. The algorithm to recognize the digital straight segments is formulated in terms of the growing pyramidal networks taking into account the conceptual model of memory and identification (Rabinovich [4]).

Key Agreement Protocol Using Elliptic Curve Matrix Power Function

* Work is partially supported by the Lithuanian State Science and Studies Foundation.

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve

2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14H40, 20M14.

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Densities with Spherical Level Sets in the Gauss-exponential Domain

2000 Mathematics Subject Classification: 60F05, 60B10.

Characterizations of Exponential Distribution via Conditional Expectations of Record Values

2000 Mathematics Subject Classification: 62G30, 62E10.

Exponential approximation in the norms and semi-norms

The deviations of some entire functions of exponential type from real-valued functions and their derivatives are estimated. As approximation metrics we use the Lp-norms and power variations on R. Theorems presented here correspond to the Ganelius and Popov results concerning the one-sided trigonometric approximation of periodic functions (see [4, 5 and 8]). Some related facts were announced in [2, 3, 6 and 7].

Characterizations of Exponential Distribution Based on Sample of Size Three

2010 Mathematics Subject Classification: 62G30, 62E10.