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The objective of this paper is to construct fractional wavelet frames in L2(ℝ). A necessary condition and four sufficient conditions for fractional wavelet frames are given by virtue of fractional Fourier transform. The proposed inequalities generalize all the classical wavelet inequalities when θ = π/2. An example is presented at the end. [ABSTRACT FROM AUTHOR]

In this study, a hybrid method based on coupling discrete wavelet transforms (DWTs) and artificial neural network (ANN) for yield spread forecasting is proposed. The discrete wavelet transform (DWT) using five different wavelet families is applied to decompose the five different yield spreads constructed at shorter end, longer end, and policy relevant area of the yield curve to eliminate noise from them. The wavelet coefficients are then used as inputs into Levenberg-Marquardt (LM) ANN models to forecast the predictive power of each of these spreads for output growth. We find that the yield spreads constructed at the shorter end and policy relevant areas of the yield curve have a better predictive power to forecast the output growth, whereas the yield spreads, which are constructed at the longer end of the yield curve do not seem to have predictive information for output growth. These results provide the robustness to the earlier results. [ABSTRACT FROM AUTHOR]

Abstract: Using classical analytic techniques, the Wilker–Anglesio inequality and parameterized Wilker inequality for hyperbolic functions are proved. The main result is then applied to deriving a hyperbolic analogue of the Sándor–Bencze inequality. [Copyright &y& Elsevier]

Abstract: Let be a given real number, and , be two parameters, and let We determine the values which provide the best approximation: Furthermore, we establish a sharp Jordan’s inequality, and then apply it to improve the Yang Le inequality. [Copyright &y& Elsevier]

This paper deals with recent developments of Hilbert-type discrete and integral inequalities by introducing kernels, weight functions, and multiparameters. Included are numerous generalizations, extensions, and refinements of Hilbert-type inequalities involving many special functions such as beta, gamma, logarithm, trigonometric, hyper-bolic, Bernoulli's functions and Bernoulli's numbers, Euler's constant, zeta function, and hypergeometric functions with many applications. Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in inequalities are the best possible. Many particular cases of Hilbert-type inequalities are presented with numerous applications. A large number of major books and recent research papers published during 2009-2012 are included to stimulate new interest in future study and research. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with a Hilbert-type linear series operator and its norm. Several generalizations of the Hilbert-type inequalities whose kernels are symmetric and homogeneous of the first order are presented. Included are applications of some new extended Hilbert-type inequalities with the best possible constant factors and the equivalent forms are established. Also, the reverse forms and some particular forms are obtained as special cases of the results of this paper. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with a new generalization of the Garfunkel–Bankoff inequality by introducing a parameter, which relaxes the conditions of the Garfunkel–Bankoff inequality. As applications, an improved version of the Finsler–Hadwiger inequality is obtained. [Copyright &y& Elsevier]

Abstract: This paper deals with a generalization of L’Hôspital-type rules for monotonicity. The result is then used to establish a class of two-sided bounding inequalities for higher-order differentiable functions. As consequences, some refined upper and lower bounds for exponential function, logarithmic function, trigonometric functions and hyperbolic functions are derived. [Copyright &y& Elsevier]

Abstract: In this work, we first prove a generalized version of a parameterized Jordan-type inequality. We then use it to prove the generalized versions of Janous’s inequality and Tsintsifas’s inequality which reduce to two inequalities conjectured by Janous and Tsintsifas as special cases. [Copyright &y& Elsevier]

Abstract: In this work, we extend Jordan’s inequality to obtain a new type of inequality involving functions and their higher-order derivatives. The result is then used to obtain some higher accurate inequalities of Jordan type. [Copyright &y& Elsevier]

Abstract: A new generalized version of Aczél’s inequality is proved. This is a unified generalization of some known results. Moreover, the result is applied to the improvement of the well-known Bellman’s inequality. [Copyright &y& Elsevier]

Abstract: In this work, a weighted generalization of Rado’s inequality and Popoviciu’s inequality is given, from which some valuable inequalities of Rado–Popoviciu type are derived. Moreover, the result is used to obtain refinements of weighted mean value inequalities. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the third order two-point generalized right focal boundary value problem A few new results are given for the existence of at least one, two, three and infinitely many monotone positive solutions of the above boundary value problem by using the Krasnosel’skii fixed-point theorem in cones, and the Leggett–Williams fixed-point theorem. [Copyright &y& Elsevier]

Abstract: This paper deals with recent developments of linear and nonlinear Rossby waves in an ocean. Included are also linear Poincaré, Rossby, and Kelvin waves in an ocean. The dispersion diagrams for Poincaré, Kelvin and Rossby waves are presented. Special attention is given to the nonlinear Rossby waves on a β-plane ocean. Based on the perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies a modified nonlinear Schrödinger equation. The solution of this equation represents solitary waves in a dispersive medium. In other words, the envelope of the amplitude of the waves has a soliton structure and these envelope solitons propagate with the group velocity of the Rossby waves. Finally, a nonlinear analytical model is presented for long Rossby waves in a meridional channel with weak shear. A new nonlinear wave equation for the amplitude of large Rossby waves is derived in a region where fluid flows over the recirculation core. It is shown that the governing amplitude equations for the inner and outer zones are both KdV type, where weak nonlinearity is balanced by weak dispersion. In the inner zone, the nonlinear amplitude equation has a new term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude, and this term occurs to account for a nonlinearity due to the flow over the vortex core. The solution of the amplitude equations with the linear shear flow represents the solitary waves. The present study deals with the lowest mode analysis. An extension of the higher modes of this work will be made in a subsequent paper. [Copyright &y& Elsevier]

Using the theory of majorization, new inequalities for convex sequences are proved. A necessary and sufficient condition for a convex sequence is established. This reveals an important relationship between the convex sequence and the majorized inequality. Finally, some applications of our new inequalities and some improvements of certain known results are presented. [Copyright &y& Elsevier]

The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for two popular models for the marginal posterior density. We also illustrate the superior performance of these models over the standard models for wavelet coefficients. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with a new generalized and sharp version of Jordan’s inequality which is a unified generalization of some known results. An application of our results to the improvement of the Yang Le inequality is provided in this paper. [Copyright &y& Elsevier]

This paper deals with the generalization and sharp versions of the Wolstenholme cyclic inequality and their applications. The inequalities of this paper improve and unify corresponding known results. Several interesting inequalities including the celebrated Ozeki inequality are obtained. Extensions of the Wolstenholme inequality for a complex polygon and the Wolstenholme inequality for a convex quadrilateral are derived. As example of applications, the well-known Erdös–Mordell inequality is improved in this paper. In addition, several extensions, unifications and refinements of Gueron–Shafrir’s inequalities and Mitrinović–Pecaric’s inequality are established. [Copyright &y& Elsevier]

Abstract: A new generalized and sharp version of Jordan’s inequality is proved and it is applied in the improvement of the Yang Le inequality. Moreover, a mistake in the proof of sharpening Jordan’s inequality due to Zhu [S.H. Wu, On generalizations and refinements of Jordan type inequality, Octogon Math. Mag. 12(1) (2004) 267–272] is corrected. [Copyright &y& Elsevier]

Abstract: Values of are determined for which there exist positive solutions of the fourth-order singular boundary value problems where , is parameter. For , we give criteria for the existence of eigenfunctions. [Copyright &y& Elsevier]

Kernel theorems for spaces of Cauchy ultradistribution, supported by an n-dimensional tube and cone of the product type, are investigated. [Copyright &y& Elsevier]

In this paper, by introducing three parameters A, B, and λ, and estimating the weight coefficient, we give a generalization of the extended Hardy–Hilbert''s inequality with a best possible constant factor, involving the β function. We also consider its equivalent inequality and the associated double series form. [Copyright &y& Elsevier]

An extension of Carlson''s inequality is made by using the Euler–Maclaurin summation formula. The integral analogues of this inequality are also presented. [Copyright &y& Elsevier]

A review of the article "A Brief Historical Development of Classical Mathematics Before the Renaissance," by Lokenath Debnath, which appeared in the journal "International Journal of Mathematical Education in Science and Technology," on July 2011, is presented.

Abstract: This paper deals with existence theorems of positive solutions for singular elliptic boundary value problems in a ball. The results of this paper are generalizations of those proved by authors cited in the references. [Copyright &y& Elsevier]

Abstract: On the basis of a special cone and the application of the fixed point theory, some new results for the existence of positive solutions of singular Sturm–Liouville boundary value problems on the half-line are obtained. [Copyright &y& Elsevier]

Abstract: The stability of a horizontal layer of fluid heated from below as well as from above is examined. The temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent part, which is oscillatory. The amplitude of temperature modulation is δ. By considering the weakly non-linear analysis, it is shown that the modulation produces a range of stable hexagons near the critical Rayleigh number. Some comparisons have been made with the other theoretical results. [Copyright &y& Elsevier]

In this paper the wavelet transformation on Gelfand and Shilov spaces of type WM(◻n), WΩ(Δn) and WΩM (Δn) is studied. it is shown that Wψϕ : WM (◻n ) → WM (◻n × ◻n+), Wψϕ WΩ (Δn) → WΩ(Δn×◻n+) and Wψϕ : WΩM (Δn) → WΩM (Δn × ◻n+) is linear and continuous where ◻n and Δn are n-dimensional real numbers and complex numbers. A boundedness result in a generalized Sobolev space is derived. [ABSTRACT FROM AUTHOR]

Abstract: Some new generalizations of the Hilbert integral inequality by introducing real functions and . The results of this paper reduce to those of the corresponding inequalities proved by Gao [Mingzhe Gao, On Hilbert''s integral inequality, Math. Appl. 11 (3) (1998) 32–35]. Some applications are considered. [Copyright &y& Elsevier]

Abstract: Under certain assumptions on the nonlinear–nonhomogenous term of ordinary differential equations associated with fourth order singular boundary value problems, we establish a necessary and sufficient condition for the existence of positive solutions of the boundary value problem by means of fixed point theorems. [Copyright &y& Elsevier]

Abstract: The linear stability of a thin vertical fluid layer heated from below is considered. Here the gravitational field consists of two parts: a constant part and a time-dependent part varying periodically. The time-dependent part has been expressed in Fourier series. The effect of gravity modulation on the fluid layer is examined. Using an asymptotic analysis the convective threshold has been determined. Some comparisons are made with the known results. [Copyright &y& Elsevier]

By the application of continuous wavelet transforms (or windowed Fourier transform) and employing Burzyk''s conjecture, the wavelet transform for integrable Boehmians is obtained. Inversion formula is also established. [Copyright &y& Elsevier]

In this paper, we give a unified generalization of the Gini means and Heronian means. The Schur-geometric convexity of the generalized Gini-Heronian means are investigated. Our result generalizes an earlier result given by Shi et al. (J. Inequal. Appl. 2008:879273, 2008). At the end of the paper, two new inequalities related to the generalized Gini-Heronian means are established to illustrate the applicability of the given result. [ABSTRACT FROM AUTHOR]