Displaying similar documents to “Existence of positive solutions for second order m-point boundary value problems”

A new characterization of symmetric group by NSE

Azam Babai, Zeinab Akhlaghi (2017)

Czechoslovak Mathematical Journal

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Let G be a group and ω ( G ) be the set of element orders of G . Let k ω ( G ) and m k ( G ) be the number of elements of order k in G . Let nse ( G ) = { m k ( G ) : k ω ( G ) } . Assume r is a prime number and let G be a group such that nse ( G ) = nse ( S r ) , where S r is the symmetric group of degree r . In this paper we prove that G S r , if r divides the order of G and r 2 does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components.

On a system of equations with primes

Paolo Leonetti, Salvatore Tringali (2014)

Journal de Théorie des Nombres de Bordeaux

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Given an integer n 3 , let u 1 , ... , u n be pairwise coprime integers 2 , 𝒟 a family of nonempty proper subsets of { 1 , ... , n } with “enough” elements, and ε a function 𝒟 { ± 1 } . Does there exist at least one prime q such that q divides i I u i - ε ( I ) for some I 𝒟 , but it does not divide u 1 u n ? We answer this question in the positive when the u i are prime powers and ε and 𝒟 are subjected to certain restrictions. We use the result to prove that, if ε 0 { ± 1 } and A is a set of three or more primes that contains all prime divisors of any...

Admissible spaces for a first order differential equation with delayed argument

Nina A. Chernyavskaya, Lela S. Dorel, Leonid A. Shuster (2019)

Czechoslovak Mathematical Journal

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We consider the equation - y ' ( x ) + q ( x ) y ( x - ϕ ( x ) ) = f ( x ) , x , where ϕ and q ( q 1 ) are positive continuous functions for all x and f C ( ) . By a solution of the equation we mean any function y , continuously differentiable everywhere in , which satisfies the equation for all x . We show that under certain additional conditions on the functions ϕ and q , the above equation has a unique solution y , satisfying the inequality y ' C ( ) + q y C ( ) c f C ( ) , where the constant c ( 0 , ) does not depend on the choice of f .

Differences of two semiconvex functions on the real line

Václav Kryštof, Luděk Zajíček (2016)

Commentationes Mathematicae Universitatis Carolinae

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It is proved that real functions on which can be represented as the difference of two semiconvex functions with a general modulus (or of two lower C 1 -functions, or of two strongly paraconvex functions) coincide with semismooth functions on (i.e. those locally Lipschitz functions on for which f + ' ( x ) = lim t x + f + ' ( t ) and f - ' ( x ) = lim t x - f - ' ( t ) for each x ). Further, for each modulus ω , we characterize the class D S C ω of functions on which can be written as f = g - h , where g and h are semiconvex with modulus C ω (for some C > 0 ) using a new...

Ramsey numbers for trees II

Zhi-Hong Sun (2021)

Czechoslovak Mathematical Journal

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Let r ( G 1 , G 2 ) be the Ramsey number of the two graphs G 1 and G 2 . For n 1 n 2 1 let S ( n 1 , n 2 ) be the double star given by V ( S ( n 1 , n 2 ) ) = { v 0 , v 1 , ... , v n 1 , w 0 , w 1 , ... , w n 2 } and E ( S ( n 1 , n 2 ) ) = { v 0 v 1 , ... , v 0 v n 1 , v 0 w 0 , w 0 w 1 , ... , w 0 w n 2 } . We determine r ( K 1 , m - 1 , S ( n 1 , n 2 ) ) under certain conditions. For n 6 let T n 3 = S ( n - 5 , 3 ) , T n ' ' = ( V , E 2 ) and T n ' ' ' = ( V , E 3 ) , where V = { v 0 , v 1 , ... , v n - 1 } , E 2 = { v 0 v 1 , ... , v 0 v n - 4 , v 1 v n - 3 , v 1 v n - 2 , v 2 v n - 1 } and E 3 = { v 0 v 1 , ... , v 0 v n - 4 , v 1 v n - 3 , v 2 v n - 2 , v 3 v n - 1 } . We also obtain explicit formulas for r ( K 1 , m - 1 , T n ) , r ( T m ' , T n ) ( n m + 3 ) , r ( T n , T n ) , r ( T n ' , T n ) and r ( P n , T n ) , where T n { T n ' ' , T n ' ' ' , T n 3 } , P n is the path on n vertices and T n ' is the unique tree with n vertices and maximal degree n - 2 .

A Diophantine inequality with four squares and one k th power of primes

Quanwu Mu, Minhui Zhu, Ping Li (2019)

Czechoslovak Mathematical Journal

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Let k 5 be an odd integer and η be any given real number. We prove that if λ 1 , λ 2 , λ 3 , λ 4 , μ are nonzero real numbers, not all of the same sign, and λ 1 / λ 2 is irrational, then for any real number σ with 0 < σ < 1 / ( 8 ϑ ( k ) ) , the inequality | λ 1 p 1 2 + λ 2 p 2 2 + λ 3 p 3 2 + λ 4 p 4 2 + μ p 5 k + η | < max 1 j 5 p j - σ has infinitely many solutions in prime variables p 1 , p 2 , , p 5 , where ϑ ( k ) = 3 × 2 ( k - 5 ) / 2 for k = 5 , 7 , 9 and ϑ ( k ) = [ ( k 2 + 2 k + 5 ) / 8 ] for odd integer k with k 11 . This improves a recent result in W. Ge, T. Wang (2018).

Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

Moshe Marcus, Laurent Véron (2004)

Journal of the European Mathematical Society

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Let Ω be a bounded domain of class C 2 in N and let K be a compact subset of Ω . Assume that q ( N + 1 ) / ( N 1 ) and denote by U K the maximal solution of Δ u + u q = 0 in Ω which vanishes on Ω K . We obtain sharp upper and lower estimates for U K in terms of the Bessel capacity C 2 / q , q ' and prove that U K is σ -moderate. In addition we describe the precise asymptotic behavior of U K at points σ K , which depends on the “density” of K at σ , measured in terms of the capacity C 2 / q , q ' .

Some theorems of Korovkin type

Tomoko Hachiro, Takateru Okayasu (2003)

Studia Mathematica

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We take another approach to the well known theorem of Korovkin, in the following situation: X, Y are compact Hausdorff spaces, M is a unital subspace of the Banach space C(X) (respectively, C ( X ) ) of all complex-valued (resp., real-valued) continuous functions on X, S ⊂ M a complex (resp., real) function space on X, ϕₙ a sequence of unital linear contractions from M into C(Y) (resp., C ( Y ) ), and ϕ a linear isometry from M into C(Y) (resp., C ( Y ) ). We show, under the assumption that Π N Π T , where Π N is...

Variations on a question concerning the degrees of divisors of x n - 1

Lola Thompson (2014)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we examine a natural question concerning the divisors of the polynomial x n - 1 : “How often does x n - 1 have a divisor of every degree between 1 and n ?” In a previous paper, we considered the situation when x n - 1 is factored in [ x ] . In this paper, we replace [ x ] with 𝔽 p [ x ] , where p is an arbitrary-but-fixed prime. We also consider those n where this condition holds for all p .

Recognition of some families of finite simple groups by order and set of orders of vanishing elements

Maryam Khatami, Azam Babai (2018)

Czechoslovak Mathematical Journal

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Let G be a finite group. An element g G is called a vanishing element if there exists an irreducible complex character χ of G such that χ ( g ) = 0 . Denote by Vo ( G ) the set of orders of vanishing elements of G . Ghasemabadi, Iranmanesh, Mavadatpour (2015), in their paper presented the following conjecture: Let G be a finite group and M a finite nonabelian simple group such that Vo ( G ) = Vo ( M ) and | G | = | M | . Then G M . We answer in affirmative this conjecture for M = S z ( q ) , where q = 2 2 n + 1 and either q - 1 , q - 2 q + 1 or q + 2 q + 1 is a prime number, and M = F 4 ( q ) , where...

Representation functions for binary linear forms

Fang-Gang Xue (2024)

Czechoslovak Mathematical Journal

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Let be the set of integers, 0 the set of nonnegative integers and F ( x 1 , x 2 ) = u 1 x 1 + u 2 x 2 be a binary linear form whose coefficients u 1 , u 2 are nonzero, relatively prime integers such that u 1 u 2 ± 1 and u 1 u 2 - 2 . Let f : 0 { } be any function such that the set f - 1 ( 0 ) has asymptotic density zero. In 2007, M. B. Nathanson (2007) proved that there exists a set A of integers such that r A , F ( n ) = f ( n ) for all integers n , where r A , F ( n ) = | { ( a , a ' ) : n = u 1 a + u 2 a ' : a , a ' A } | . We add the structure of difference for the binary linear form F ( x 1 , x 2 ) .

On the distribution of ( k , r ) -integers in Piatetski-Shapiro sequences

Teerapat Srichan (2021)

Czechoslovak Mathematical Journal

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A natural number n is said to be a ( k , r ) -integer if n = a k b , where k > r > 1 and b is not divisible by the r th power of any prime. We study the distribution of such ( k , r ) -integers in the Piatetski-Shapiro sequence { n c } with c > 1 . As a corollary, we also obtain similar results for semi- r -free integers.

Repdigits in the base b as sums of four balancing numbers

Refik Keskin, Faticko Erduvan (2021)

Mathematica Bohemica

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The sequence of balancing numbers ( B n ) is defined by the recurrence relation B n = 6 B n - 1 - B n - 2 for n 2 with initial conditions B 0 = 0 and B 1 = 1 . B n is called the n th balancing number. In this paper, we find all repdigits in the base b , which are sums of four balancing numbers. As a result of our theorem, we state that if B n is repdigit in the base b and has at least two digits, then ( n , b ) = ( 2 , 5 ) , ( 3 , 6 ) . Namely, B 2 = 6 = ( 11 ) 5 and B 3 = 35 = ( 55 ) 6 .