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In the present investigation, we introduce a new class of meromorphic functions defined in the punctured unit disk Δ * : = { ϑ ∈ C : 0 < | ϑ | < 1 } by making use of the Erdély–Kober operator I ς , ϱ τ , κ which unifies well-known classes of the meromorphic uniformly convex function with positive coefficients. Coefficient inequalities, growth and distortion inequalities, in addition to closure properties are acquired. We also set up a few outcomes concerning convolution and the partial sums of meromorphic functions in this new class. We additionally state some new subclasses and its characteristic houses through specializing the parameters that are new and no longer studied in association with the Erdély–Kober operator thus far. [ABSTRACT FROM AUTHOR]

We give a criterion which characterizes a real multi-variate Laurent polynomial with full-dimensional smooth Newton polytope to have the property that all sufficiently large powers of the polynomial have fully positive coefficients. Here a Laurent polynomial is said to have fully positive coefficients if the coefficients of its monomial terms indexed by the lattice points of its Newton polytope are all positive. Our result generalizes an earlier result of Colin Tan and the author, which corresponds to the special case when the Newton polytope of the Laurent polynomial is a translate of a standard simplex. The result also generalizes a result of De Angelis, which corresponds to the special case of univariate polynomials. As an application, we also give a characterization of certain polynomial spectral radius functions of the defining matrix functions of Markov chains. [ABSTRACT FROM AUTHOR]

In the present investigation, we introduce a new class of meromorphic functions defined in the punctured unit disk Δ*:={ϑ∈C:0<|ϑ|<1} by making use of the Erdély–Kober operator Iς,ϱτ,κ which unifies well-known classes of the meromorphic uniformly convex function with positive coefficients. Coefficient inequalities, growth and distortion inequalities, in addition to closure properties are acquired. We also set up a few outcomes concerning convolution and the partial sums of meromorphic functions in this new class. We additionally state some new subclasses and its characteristic houses through specializing the parameters that are new and no longer studied in association with the Erdély–Kober operator thus far.

We prove that the determinant of a matrix polynomial with Hermitian positive definite (semidefinite) coefficients is a polynomial with positive (nonnegative) coefficients. [ABSTRACT FROM AUTHOR]

A coherent interference‐free tunable microwave photonic notch filter with a pair of negative and positive coefficients generated by employing polarisation multiplexing and cross gain modulation in a semiconductor optical amplifier is proposed and demonstrated through simulation results. The negative and positive coefficients of the notch filter are realised through two orthogonal polarisation states of a single continuous wave laser diode. The free spectral range of microwave photonic filter is tuned by varying the differential group delay of a birefringent single‐mode fibre. The proposed filter shows good tunability, easy implementation and is cost‐effective. [ABSTRACT FROM AUTHOR]

We prove that generalized exponential splitting methods making explicit use of commutators of the vector fields are limited to order four when only real coefficients are admitted. This generalizes the restriction to order two for classical splitting methods with only positive coefficients. [ABSTRACT FROM AUTHOR]

In this paper the authors introduced a new generalized differintegral operator for meromorphic univalent functions in U* = {z : z ∈ C, 0 < |z| < 1}. The objective of this paper is to establish certain results concerning the Hadamard product of functions in the classes ∑^{∗,m}_{μ,λ} (α, β , γ, k) and ∑^h_{μ,λ} (α, β , γ, k).

We give a criterion which characterizes a homogeneous real multivariate polynomial to have the property that all sufficiently large powers of the polynomial (as well as their products with any given positive homogeneous polynomial) have all positive coefficients. Our result generalizes a result of De Angelis, which corresponds to the case of homogeneous bivariate polynomials, as well as a classical result of Pólya, which corresponds to the case of a specific linear polynomial. As an application, we also give a characterization of certain polynomial spectral radius functions of the defining matrix functions of Markov chains. [ABSTRACT FROM AUTHOR]

Let p be a nonconstant form in $${\mathbb {R}}[x_1,\ldots ,x_n]$$ with $$p(1,\ldots ,1)>0$$ . If $$p^m$$ has strictly positive coefficients for some integer $$m\ge 1$$ , we show that $$p^m$$ has strictly positive coefficients for all sufficiently large m. More generally, for any such p and any form q that is strictly positive on $$({\mathbb {R}}_+)^n{\setminus }\{0\}$$ , we show that the form $$p^mq$$ has strictly positive coefficients for all sufficiently large m. This result can be considered as a strict Positivstellensatz for forms relative to $$({\mathbb {R}}_+)^n{\setminus }\{0\}$$ . We give two proofs, one based on results of Handelman, the other on techniques from real algebra. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to introduce a new subclass of meromorphic functions with positive and .xed second coefficients by means of Rafid-operator by fixing second coefficient. We give a necessary and sufficient condition for a function f to be in this class. Also we obtain coefficient inequality, distortion properties, meromorphically radii of close-to-convexity, starlikeness and convexity, extreme points, convex linear combinations, for the functions f in this class. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new class of meromorphic multivalent functions Σ*p(k, α, β) with positive coefficients. The main object of the present paper is to prove some properties for functions belonging to the class Σ*p(k, α, β). [ABSTRACT FROM AUTHOR]

In the present paper, we consider the new subclass of Meromorphic functions with positive coefficients and obtain a necessary and sufficient condition for a function f to be in this class. We obtain distortion properties, radius of convexity, starlikeness, convex linear combinations for the function f in this class. [ABSTRACT FROM AUTHOR]

In this paper we study the mapping properties with respect to new generalised integral operator which was studied recently. [ABSTRACT FROM AUTHOR]

In this paper we study the subordination of a certain subclass of convex functions with negative coefficients. [ABSTRACT FROM AUTHOR]

Abstract: In this work the authors extend certain results concerning the Hadamard product for two classes related to starlike and convex univalent meromorphic functions with positive coefficients by using convolution. [Copyright &y& Elsevier]

Abstract: In the Sobolev space optimal quadrature formulas of the form with the nodes are investigated. For optimal coefficients explicit forms are obtained and the norm of the error functional is calculated for any natural numbers and . In particular, in the case and for optimal quadrature formulas with positive coefficients are numerically obtained and some of them are compared with well-known optimal formulas. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the authors establish certain results concerning the Hadamard product for two classes related to starlike and convex univalent meromorphic functions of order and type with positive coefficients. [Copyright &y& Elsevier]

Abstract: The main object of the present paper is to introduce certain novel classes of meromorphic multivalent functions , and . In this paper, we obtain coefficient estimates, distortion theorems, radii of convexity and closure theorems for the class . Several interesting results involving the Hadamard product of functions belonging to the classes and are also derived. Also integral transforms of functions in the classes and are studied. [Copyright &y& Elsevier]

A continuously tunable photonic microwave bandpass filter with positive and negative coefficients implemented using an optical phase modulator and chirped fiber Bragg gratings (FBGs) is proposed and experimentally demonstrated. The positive and negative coefficients are generated through optical phase-modulation to intensity-modulation conversion by reflecting the phase-modulated optical carrier from linearly chirped FBGs (LCFBGs) with positive and negative dispersions. The tunability of the filter is realized by changing the wavelength of the optical carrier such that it is reflected at different physical locations in the LCFBGs. A two-tap microwave bandpass filter with a free spectral range tunable from 1.14 to 4.55 GHz is experimentally demonstrated. [ABSTRACT FROM PUBLISHER]

Abstract: G. Andrews proved that if n is a prime number then the coefficients and of the product have the same sign, see [G. Andrews, On a conjecture of Peter Borwein, J. Symbolic Comput. 20 (1995) 487–501]. We generalize this result in several directions. Our results are based on the observation that many products can be written as alternating sums of characters of Virasoro modules. [Copyright &y& Elsevier]