Abstract Cauchy problem for the Bessel–Struve equation

We consider the Cauchy problem for the Bessel–Struve equation in a Banach space. A sufficient condition for the solvability of this problem is proved, and the solution operator is written in explicit form via the Bessel and Struve operator functions. A number of properties is established for the solutions.     

A Wiener–Wintner theorem for the Hilbert transform

We prove the following extension of the Wiener–Wintner theorem and the Carleson theorem on pointwise convergence of Fourier series: For all measure-preserving flows (X,μ,T _t ) and f∈L ^p (X,μ), there is a set X _f ⊂X of probability one, so that for all x∈X _f ,

Liouville theorems for the Navier–Stokes equations and applications

We study bounded ancient solutions of the Navier–Stokes equations. These are solutions with bounded velocity defined in R ⁿ × (−1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios of potential singularity formation for axi-symmetric solutions, and obtain extensions of results in a recent paper by Chen, Strain, Tsai and Yau [4].     

Estimate of the Fourier–Bessel Multipliers for the Poly-axially Operator

We prove the analogue of H?rmander–Mikhlin multiplier theorem for the multidimensional Fourier–Bessel transform associated with the Poly-axially operator.     

Turán-type inequalities for Struve,modified Struve and Anger–Weber functions

The aim of this paper is to establish the Turán-type inequalities for Struve functions, modified Struve functions, Anger–Weber functions and Hurwitz zeta function, by using a new form of the Cauchy–Bunyakovsky–Schwarz inequality.     

Paley–Wiener theorem for the Weinstein transform and applications

In this paper our aim is to establish the Paley–Wiener Theorem for the Weinstein Transform. Furthermore, some applications are presents. In particular some properties for the generalized translation operator associated with the Weinstein operator are proved, an integral representation and a series representation for a function in the Paley–Wiener classes are investigated.     

Oscillation and non-oscillation theorems for superlinear Emden–Fowler equations of the fourth order

We study the oscillatory behavior of solutions of the fourth-order Emden–Fowler equation: (E) y^(iv)+q(t)|y|sgny=0, where >1 and q(t) is a positive continuous function on [t₀,), t₀>0. Our main results Theorem 2 – if (q(t)t^(3+5)/2)0, then equation (E) has oscillatory solutions; Theorem 3 – if lim_tq(t)t^4+(-1)=0, >0, then every solution y(t) of equation (E) is either non-oscillatory or satisfies limsup_tt^-+i|y⁽ⁱ⁾(t)|= for < and i=0,1,2,3,4. These results complement those given by Kura for equation (E) when q(t)<0 and provide analogues to the results of the second-order equation, y+q(t)|y|sgny=0,>1. Mathematics Subject Classification (2000) 34C10, 34C15     

A new variant of the Schwarz–Pick–Ahlfors Lemma

We prove a “general shrinking lemma” that resembles the Schwarz–Pick–Ahlfors Lemma and its many generalizations, but differs in applying to maps of a finite disk into a disk, rather than requiring the domain of the map to be complete. The conclusion is that distances to the origin are all shrunk, and by a limiting procedure we can recover the original Ahlfors Lemma, that all distances are shrunk. The method of proof is also different in that it relates the shrinking of the Schwarz–Pick–Ahlfors-type lemmas to the comparison theorems of Riemannian geometry. Received: 26 May 1998 / Revised version: 4 May 1999     

A new look at the John–Nirenberg and John–Strömberg theorems for BMO

We develop some techniques for studying various versions of the function space BMO. Special cases of one of our results give alternative proofs of the celebrated John–Nirenberg inequality and of related inequalities due to John and to Wik. Our approach enables us to pose a simply formulated “geometric” question, for which an affirmative answer would lead to a version of the John–Nirenberg inequality with dimension free constants.     

Finiteness theorems for the shifted Witt and higher Grothendieck–Witt groups of arithmetic schemes

For smooth varieties over finite fields, we prove that the shifted (aka derived) Witt groups of surfaces are finite and the higher Grothendieck–Witt groups (aka Hermitian K-theory) of curves are finitely generated. For more general arithmetic schemes, we give conditional results, for example, finite generation of the motivic cohomology groups implies finite generation of the Grothendieck–Witt groups.     

A remark on the Brauer–Fowler theorems

Archiv der Mathematik - Let G be a finite group of even order that has no 2-rank 1. We will prove, using only elementary methods, that there is an involution $$t in G$$ such that $$|G| &lt;...     

A comparison between the reduced differential transform method and the Adomian decomposition method for the Newell–Whitehead–Segel equation

In this paper, we will carry out a comparative study between the reduced differential transform method and the Adomian decomposition method. This is been achieved by handling the Newell–Whitehead–Segel equation. Two numerical examples have also been carried out to validate and demonstrate efficiency of the two methods. Furthermost, it is shown that the reduced differential transform method has an advantage over the Adomian decomposition method that it takes less time to solve the nonlinear problems without using the Adomian polynomials.     

Some generalizations of Bessel and Flett potentials associated to the Laplace–Bessel differential operator

We introduce the notion of bi-parametric potential-type operators, which generalize the Bessel and Flett potentials associated to singular Laplace–Bessel differential operator. Explicit inversion formulas for them are obtained by using a special wavelet-like transform, generated by the so-called ‘modified beta-semigroup’.     

A compact variant of the QCR method for quadratically constrained quadratic 0–1 programs

Quadratic Convex Reformulation (QCR) is a technique that was originally proposed for quadratic 0–1 programs, and then extended to various other problems. It is used to convert non-convex instances into convex ones, in such a way that the bound obtained by solving the continuous relaxation of the reformulated instance is as strong as possible. In this paper, we focus on the case of quadratically constrained quadratic 0–1 programs. The variant of QCR previously proposed for this case involves the addition of a quadratic number of auxiliary continuous variables. We show that, in fact, at most one additional variable is needed. Some computational results are also presented.     

Generalization of the theorems of Barndorff-Nielsen and Balakrishnan–Stepanov to Riesz spaces

Positivity - In a Dedekind complete Riesz space, E, we show that if $$(P_n)$$ is a sequence of band projections in E then $$begin{aligned} limsup limits _{nrightarrow infty } P_n - liminf...