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## You are looking at 1 - 100 of 11,027 items

## Abstract

We provide a Maltsev characterization of congruence distributive varieties by showing that a variety 𝓥 is congruence distributive if and only if the congruence identity *k* factors) holds in 𝓥, for some natural number *k*.

## Abstract

Fix 2 < n < ω and let CA_{n} denote the class of cyindric algebras of dimension n. Roughly CA_{n} is the algebraic counterpart of the proof theory of first order logic restricted to the first *n* variables which we denote by L_{n}. The variety RCA_{n} of representable CA_{n}s reflects algebraically the semantics of *L*
_{n}. Members of RCA_{n} are concrete algebras consisting of genuine n-ary relations, with set theoretic operations induced by the nature of relations, such as projections referred to as cylindrifications. Although CA_{n} has a finite equational axiomatization, RCA_{n} is not finitely axiomatizable, and it generally exhibits wild, often unpredictable and unruly behavior. This makes the theory of CA_{n} substantially richer than that of Boolean algebras, just as much as L_{ω,ω} is richer than propositional logic. We show using a so-called blow up and blur construction that several varieties (in fact infinitely many) containing and including the variety RCA_{n} are not atom-canonical. A variety V of Boolean algebras with operators is atom canonical, if whenever **𝔄**
*L*
_{ω,ω}, fails dramatically for *L*
_{n} even if we allow certain generalized models that are only locallly clasfsical. It is also shown that any class K such that _{n} is the class of completely representable CA_{n}s, and S_{c} denotes the operation of forming dense (complete) subalgebras, is not elementary. Finally, we show that any class K such that _{d} denotes the operation of forming dense subalgebra.

## Abstract

Let **𝔄** be a unital Banach algebra and **ℜ** its Jacobson radical. This paper investigates Banach algebras satisfying some chain conditions on closed ideals. In particular, it is shown that a Banach algebra **𝔄** satisfies the descending chain condition on closed left ideals then **𝔄**/**ℜ** is finite dimensional. We also prove that a *C*
^{*}-algebra satisfies the ascending chain condition on left annihilators if and only if it is finite dimensional. Moreover, other auxiliary results are established.

## Abstract

We give two new simple characterizations of the Cauchy distribution by using the Möbius and Mellin transforms. They also yield characterizations of the circular Cauchy distribution and the mixture Cauchy model.

## Abstract

In this paper we present different variants of the well-known Hermite–Hadamard inequality, in a generalized context. We consider general fractional integral operators for *h*-convex and *r*-convex functions.

## Abstract

In this study, a normalized form of regular Coulomb wave function is considered. By using the differential subordinations method due to Miller and Mocanu, we determine some conditions on the parameters such that the normalized regular Coulomb wave function is lemniscate starlike and exponential starlike in the open unit disk, respectively. In additon, by using the relationship between the regular Coulomb wave function and the Bessel function of the first kind we give some conditions for which the classical Bessel function of the first kind is lemniscate and exponential starlike in the unit disk 𝔻.

## Abstract

This survey revisits Jenő Egerváry and Otto Szász’s article of 1928 on trigonometric polynomials and simple structured matrices focussing mainly on the latter topic. In particular, we concentrate on the spectral theory for the first type of the matrices introduced in the article, which are today referred to as *k*-tridiagonal matrices, and then discuss the explosion of interest in them over the last two decades, most of which could have benefitted from the seminal article, had it not been overlooked.

## Abstract

Let *K* = ℚ(*α*) be a number field generated by a complex root *α* of a monic irreducible polynomial *f*(*x*) = *x*
^{24} – *m*, with *m* ≠ 1 is a square free rational integer. In this paper, we prove that if *m* ≡ 2 or 3 (mod 4) and *m* ≢∓1 (mod 9), then the number field *K* is monogenic. If *m* ≡ 1 (mod 4) or *m* ≡ 1 (mod 9), then the number field *K* is not monogenic.

## Abstract

In this study, we investigate suborbital graphs *G*
_{u,n} of the normalizer Γ_{B} (*N*) of Γ_{0} (*N*) in *PSL*(2, ℝ) for *N* = 2^{α}3^{β} where *α* = 1, 3, 5, 7, and *β* = 0 or 2. In these cases the normalizer becomes a triangle group and graphs arising from the action of the normalizer contain quadrilateral circuits. In order to obtain graphs, we first define an imprimitive action of Γ_{B} (*N*) on *N*) and then obtain some properties of the graphs arising from this action.

## Abstract

For *n,m*≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of *n*-linear forms on *n*-linear forms. First we classify the extreme points of the unit balls of

and

which answers the questions in [].

## Abstract

Consider the sequence *s* of the signs of the coefficients of a real univariate polynomial *P* of degree *d*. Descartes’ rule of signs gives compatibility conditions between *s* and the pair (*r*
^{+}
*,r*
^{−}), where *r*
^{+} is the number of positive roots and *r*
^{−} the number of negative roots of *P*. It was recently asked if there are other compatibility conditions, and the answer was given in the form of a list of incompatible triples (*s*; *r*
^{+}
*,r*
^{−}) which begins at degree *d* = 4 and is known up to degree 8. In this paper we raise the question of the compatibility conditions for *i*-th derivative of *P*. We prove that up to degree 5, there are no other compatibility conditions than the Descartes conditions, the above recent incompatibilities for each *i*, and the trivial conditions given by Rolle’s theorem.

## Abstract

Let *l,m,r* be fixed positive integers such that 2*l*, 3*lm*, *l > r* and 3 | *r*. In this paper, using the BHV theorem on the existence of primitive divisors of Lehmer numbers, we prove that if min{*rlm*
^{2} − 1*,*(*l* − *r*)*lm*
^{2} + 1} *>* 30, then the equation (*rlm*
^{2} − 1)^{x} + ((*l* − *r*)*lm*
^{2} + 1)^{y} = (*lm*)^{z} has only the positive integer solution (*x,y,z*) = (1*,*1*,*2).

## Abstract

In 1975 C. F. Chen and C. H. Hsiao established a new procedure to solve initial value problems of systems of linear differential equations with constant coefficients by Walsh polynomials approach. However, they did not deal with the analysis of the proposed numerical solution. In a previous article we study this procedure in case of one equation with the techniques that the theory of dyadic harmonic analysis provides us. In this paper we extend these results through the introduction of a new procedure to solve initial value problems of differential equations with not necessarily constant coefficients.

## Abstract

Let *n*. Further, let*p*(*z*) ≡ *z*^{n}*p*(1*/z*). In this paper we obtain some inequalites in this direction for polynomials that belong to this class and have all their coefficients in any sector of opening *γ*, where 0 *γ < π*. Our results generalize and sharpen several of the known results in this direction, including those of Govil and Vetterlein [3], and Rahman and Tariq [12]. We also present two examples to show that in some cases the bounds obtained by our results can be considerably sharper than the known bounds.

## Abstract

In this paper, we prove that if *X* is a space with a regular *G*
_{δ}-diagonal and *X*
^{2} is star Lindelöf then the cardinality of *X* is at most 2^{c}. We also prove that if *X* is a star Lindelöf space with a symmetric *g*-function such that *g*
^{2}(*n, x*): *n* ∈ *ω*} = {*x*} for each *x* ∈ *X* then the cardinality of *X* is at most 2^{c}. Moreover, we prove that if *X* is a star Lindelöf Hausdorff space satisfying *Hψ*(*X*) = *κ* then *e*(*X*) ^{2κ}; and if *X* is Hausdorff and *we*(*X*) = *Hψ*(*X*) = *κ*subset of a space then *e*(*X*) ^{κ}. Finally, we prove that under *V* = *L* if *X* is a first countable DCCC normal space then *X* has countable extent; and under MA+¬CH there is an example of a first countable, DCCC and normal space which is not star countable extent. This gives an answer to the Question 3.10 in *Spaces with property* (*DC*(*ω*
_{1})), *Comment. Math. Univ. Carolin.*, **58(1)** (2017), 131-135.

## Abstract

Fejes Tóth [] studied approximations of smooth surfaces in three-space by piecewise flat triangular meshes with a given number of vertices on the surface that are optimal with respect to Hausdorff distance. He proves that this Hausdorff distance decreases inversely proportional with the number of vertices of the approximating mesh if the surface is convex. He also claims that this Hausdorff distance is inversely proportional to the *square* of the number of vertices for a specific non-convex surface, namely a one-sheeted hyperboloid of revolution bounded by two congruent circles. We refute this claim, and show that the asymptotic behavior of the Hausdorff distance is linear, that is the same as for convex surfaces.

## Abstract

Let *H*
_{n} be the *n*-th harmonic number and let *v*
_{n} be its denominator. It is known that *v*
_{n} is even for every integer *H*
_{n} and prove that for any integer *n*, *v*
_{n} = *e*
^{n(1+o(1))}. In addition, we obtain some results of the logarithmic density of harmonic numbers.

## Abstract

We verify an upper bound of Pach and Tóth from 1997 on the midrange crossing constant. Details of their

## Abstract

Let 0 *< γ*
_{1}
*< γ*
_{2}
*<* ··· ⩽ ··· be the imaginary parts of non-trivial zeros of the Riemann zeta-function. In the paper, we consider the approximation of analytic functions by shifts of the Hurwitz zeta-function *ζ*(*s* + *iγ*
_{k}
*h, α*), *h >* 0, with parameter *α* such that the set {log(*m* + *α*): *m* ∈ *γ*
_{k}} is applied.

## Abstract

We study certain subgroups of the full group of Hopf algebra automorphisms of twisted tensor biproducts.

## Abstract

In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class *A _{p}* by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝ

*are obtained.*

^{n}## Abstract

Let *X* be a Hilbert *C**-module over a *C**-algebra *B*. In this paper we introduce two classes of operator algebras on the Hilbert *C**-module *X* called operator algebras with property *B* and *X*. Some of our results generalize the previous results. Also we investigate some properties of these classes of operator algebras.

## Abstract

Let *m* ≠ 0, ±1 and *n* ≥ 2 be integers. The ring of algebraic integers of the pure fields of type *n* = 2, 3,4. It is well known that for *n* = 2, an integral basis of the pure quadratic fields can be given parametrically, by using the remainder of the square-free part of m modulo 4. Such characterisation of an integral basis also exists for cubic and quartic pure fields, but for higher degree pure fields there are only results for special cases.

In this paper we explicitly give an integral basis of the field *n*.

## Abstract

Two classes of trigonometric sums about integer powers of secant function are evaluated that are closely related to Jordan's totient function.

## Abstract

We provide a new proof of Hua's result that every sufficiently large integer *N* ≡ 5 (mod 24) can be written as the sum of the five prime squares. Hua's original proof relies on the circle method and uses results from the theory of *L*-functions. Here, we present a proof based on the transference principle first introduced in[5]. Using a sieve theoretic approach similar to ([10]), we do not require any results related to the distributions of zeros of *L*- functions. The main technical difficulty of our approach lies in proving the pseudo-randomness of the majorant of the characteristic function of the *W*-tricked primes which requires a precise evaluation of the occurring Gaussian sums and Jacobi symbols.

## Abstract

For each even classical pretzel knot *P*(2*k*
_{1} + 1, 2*k*
_{2} + 1, 2*k*
_{3}), we determine the character variety of irreducible SL (2, ℂ)-representations, and clarify the steps of computing its A-polynomial.

## Abstract

We present a technique to construct Cohen–Macaulay graphs from a given graph; if this graph fulfills certain conditions. As a consequence, we characterize Cohen–Macaulay paths.

## Abstract

We prove that, for any cofinally Polish space *X*, every locally finite family of non-empty open subsets of *X* is countable. It is also established that Lindelöf domain representable spaces are cofinally Polish and domain representability coincides with subcompactness in the class of *σ*-compact spaces. It turns out that, for a topological group *G* whose space has the Lindelöf Σ-property, the space *G* is domain representable if and only if it is Čech-complete. Our results solve several published open questions.

## Abstract

Let *N* be a positive integer, *N* is called an *α-Korselt number* (equivalently *α* is said an *N-Korselt base*) if *α*
_{2}
*p* − *α*
_{1} divides *α*
_{2}
*N* − *α*
_{1} for every prime divisor *p* of *N.* By the *Korselt set* of *N* over *N* is an *α*-Korselt number.

In this paper we determine explicitly for a given prime number *q* and an integer *l* ∈ ℕ \{0, 1}, the set *q ^{l}* -Korselt bases in ℚ and others in ℤ. The case of

*l*= 2.

Moreover, we show that each nonzero rational *α* is an *N*-Korselt base for infinitely many numbers *N* = *q ^{l}* where

*q*is a prime number and

*l*∈ ℕ.

## Abstract

Sufficient conditions on associated parameters *p, b* and *c* are obtained so that the generalized and “normalized” Bessel function *u _{p}*(

*z*) =

*u*(

_{p,b,c}*z*) satisfies the inequalities ∣(1 + (

*zu*″

*(*

_{p}*z*)/

*u*′

*(*

_{p}*z*)))

^{2}− 1∣ < 1 or ∣((

*zu*

_{p}(

*z*))′/

*u*(

_{p}*z*))

^{2}− 1∣ < 1. We also determine the condition on these parameters so that $$-(4(p+(b+1)/2)/c){u}_{p}^{\text{'}}(x)\prec \sqrt{1+z}$$. Relations between the parameters

*μ*and

*p*are obtained such that the normalized Lo

__mmel__function of first kind

*h*(

_{μ,p}*z*) satisfies the subordination $$1+(z{h}_{\mu ,p}^{\text{'}\text{'}}(z)/{h}_{\mu ,q}^{\text{'}}(z))\prec \sqrt{1+z}$$. Moreover, the properties of Alexander transform of the function

*h*(

_{μ,p}*z*) are discussed.

## Abstract

In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of the variance of the best linear unbiased estimator (BLUE) for the unknown mean of a stationary sequence possessing a spectral density. In particular, we show that a necessary condition for variance of BLUE to decrease to zero exponentially is that the spectral density vanishes on a set of positive Lebesgue measure in any vicinity of zero.

## Abstract

We prove completeness, interpolation, decidability and an omitting types theorem for certain multi-dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach is algebraic addressing varieties generated by complex algebras of Kripke semantics for such logics. The algebras dealt with are common cylindrification free reducts of cylindric and polyadic algebras. For finite dimensions, we show that such varieties are finitely axiomatizable, have the super amalgamation property, and that the subclasses consisting of only completely representable algebras are elementary, and are also finitely axiomatizable in first order logic. Also their modal logics have an *N P* complete satisfiability problem. Analogous results are obtained for infinite dimensions by replacing finite axiomatizability by finite schema axiomatizability.

## Abstract

The Pell sequence *P _{n}* = 2

*P*

_{n}_{−1}+

*P*

_{n}_{−2}with initial condition

*P*

_{0}= 0,

*P*

_{1}= 1 and its associated Pell-Lucas sequence

*Q*

_{0}

*=*2,

*Q*

_{1}= 2. Here we show that 6 is the only perfect number appearing in these sequences. This paper continues a previous work that searched for perfect numbers in the Fibonacci and Lucas sequences.

## Abstract

We record an implication between a recent result due to Li, Pratt and Shakan and large gaps between arithmetic progressions.

## Abstract

We study the discrete time risk process modelled by the skip-free random walk and derive results connected to the ruin probability and crossing a fixed level for this type of process. We use the method relying on the classical ballot theorems to derive the results for crossing a fixed level and compare them to the results known for the continuous time version of the risk process. We generalize this model by adding a perturbation and, still relying on the skip-free structure of that process, we generalize the previous results on crossing the fixed level for the generalized discrete time risk process. We further derive the famous Pollaczek-Khinchine type formula for this generalized process, using the decomposition of the supremum of the dual process at some special instants of time.

## Abstract

In this paper, it has been investigated that how various stronger notions of sensitivity like 𝓕-sensitive, multi-𝓕-sensitive, (𝓕_{1}, 𝓕_{2})-sensitive, etc., where 𝓕, 𝓕_{1}, 𝓕_{2} are Furstenberg families, are carried over to countably infinite product of dynamical systems having these properties and vice versa. Similar results are also proved for induced hyperspaces.

## Abstract

We prove: For all natural numbers n and real numbers *x* ∈ [0, π] we have

The sign of equality holds if and only if *n* = 2 and *x* = 4π/5.

## Abstract

Let Vect (ℝℙ^{1}) be the Lie algebra of smooth vector fields on ℝℙ^{1}. In this paper, we classify ^{1}) to ^{1}) with coefficients in

## Abstract

To a branched cover *f* between orientable surfaces one can associate a certain *branch datum*
*f* such that *how many* these *f*'s exist, but one must of course decide what restrictions one puts on such *f*’s, and choose an equivalence relation up to which one regards them. As it turns out, quite a few natural choices for this relation are possible. In this short note we carefully analyze all these choices and show that the number of actually distinct ones is only three. To see that these three choices are indeed different from each other we employ Grothendieck's *dessins d'enfant.*

## Abstract

The aim of this paper is to study the congruences on abundant semigroups with quasi-ideal adequate transversals. The good congruences on an abundant semigroup with a quasi-ideal adequate transversal *S*° are described by the equivalence triple abstractly which consists of equivalences on the structure component parts *I, S*° and Λ. Also, it is shown that the set of all good congruences on this kind of semigroup forms a complete lattice.

## Abstract

We prove that in the category of firm acts over a firm semigroup monomorphisms co-incide with regular monomorphisms and we give an example of a non-injective monomorphism in this category. We also study conditions under which monomorphisms are injective and we prove that the lattice of subobjects of a firm act over a firm semigroup is isomorphic to the lattice unitary subacts of that act.

## Abstract

Let {*P _{n}*}

_{n≥0}be the sequence of Padovan numbers defined by

*P*

_{0}= 0,

*P*

_{1}= 1,

*P*

_{2}= 1, and

*P*

_{n}_{+3}=

*P*

_{n}_{+1}+

*P*for all

_{n}*n*≥ 0. In this paper, we find all integers

*c*admitting at least two representations as a difference between a Padovan number and a power of 3.

## Abstract

By making use of the pre-Schwarzian norm given by

*α*and type

*β*. We also employ an entirely new method to generalize and extend the results of Theorems 1, 2 and 3 in . Finally, some inequalities concerning the norm of the pre-Schwarzian derivative for Dziok-Srivastava operator are also considered.

## Abstract

For *β* an ordinal, let PEA_{β} (SetPEA_{β}) denote the class of polyadic equality (set) algebras of dimension *β*. We show that for any infinite ordinal *α*, if *n* <* ω*, the *n*-neat reduct of _{n} (regardless of the representability of *f _{a}*(

*a*) ≠ 0 and

_{∞,ω}. Various notions of representability (such as ‘satisfying the Lyndon conditions’, weak and strong) are lifted from the level of atom structures to that of atomic algebras and are further characterized via special neat embeddings. As a sample, we show that the class of atomic CA

_{n}s satisfying the Lyndon conditions coincides with the class of atomic algebras in

**ElS**

_{c}

**Nr**

_{n}

**CA**

_{ω}, where

**El**denotes ‘elementary closure’ and

**S**

_{c}is the operation of forming complete subalgebras.

## Abstract

Let {*X _{n}*:

*n*≧ 1} be a sequence of dependent random variables and let {

*w*: 1 ≦

_{nk}*k*≦

*n, n*≧ 1} be a triangular array of real numbers. We prove the almost sure version of the CLT proved by Peligrad and Utev [7] for weighted partial sums of mixing and associated sequences of random variables, i.e.

## Abstract

It is shown that if *N*(*R*) is a Lie ideal of *R* (respectively Jordan ideal and *R* is 2-torsion-free), then *N*(*R*) is an ideal. Also, it is presented a characterization of Noetherian NR rings with central idempotents (respectively with the commutative set of nilpotent elements, the Abelian unit group, the commutative commutator set).

## Abstract

In this paper we establish the boundedness of commutators of sublinear operators in weighted grand Morrey spaces. The sublinear operators under consideration contain integral operators such as Hardy-Littlewood and fractional maximal operators, Calderón-Zygmund operators, potential operators etc. The operators and spaces are defined on quasi-metric measure spaces with doubling measure.

## Abstract

In this article, the eigenvalues and eigenvectors of positive binomial operators are presented. The results generalize the previously obtained ones related to Bernstein operators. Illustrative examples are supplied.

## Abstract

A group *G* is called metahamiltonian if all its non-abelian subgroups are normal. The aim of this paper is to investigate the structure of uncountable groups of cardinality ℵ in which all proper subgroups of cardinality ℵ are metahamiltonian. It is proved that such a group is metahamiltonian, provided that it has no simple homomorphic images of cardinality ℵ. Furthermore, the behaviour of elements of finite order in uncountable groups is studied in the second part of the paper.

## Abstract

We study some mathematical properties of a new generator of continuous distributions called the Odd Nadarajah-Haghighi (ONH) family. In particular, three special models in this family are investigated, namely the ONH gamma, beta and Weibull distributions. The family density function is given as a linear combination of exponentiated densities. Further, we propose a bivariate extension and various characterization results of the new family. We determine the maximum likelihood estimates of ONH parameters for complete and censored data. We provide a simulation study to verify the precision of these estimates. We illustrate the performance of the new family by means of a real data set.

## Abstract

The intersection of all maximal right ideals of a near-ring *N* is called the quasi-radical of *N*. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials *R*
_{0}[*x*] equals to the set of all nilpotent elements of *R*
_{0}[*x*], when *R* is a commutative ring with Nil (*R*)^{2} = 0. Then we show that the quasi-radical of *R*
_{0}[*x*] is a subset of the intersection of all maximal left ideals of *R*
_{0}[*x*]. Also, we give an example to show that for some commutative ring R the quasi-radical of *R*
_{0}[*x*] coincides with the intersection of all maximal left ideals of *R*
_{0}[*x*]. Moreover, we prove that the quasi-radical of *R*
_{0}[*x*] is the greatest quasi-regular (right) ideal of it.

## Abstract

Let *G* be a finite group and *H* a subgroup of *G.* We say that *H* is an *ℌ*-subgroup of *G* if *N _{G}* (

*H*) ∩

*H*≤

^{g}*H*for all

*g*∈

*G*;

*H*is called weakly

*ℌ*-embedded in

*G*if

*G*has a normal subgroup

*K*such that

*H*=

^{G}*HK*and

*H*∩

*K*is an

*ℌ*-subgroup of

*G*, where

*H*is the normal clousre of

^{G}*H*in

*G*, i. e.,

*H*= 〈

^{G}*H*|

^{g}*g*∈

*G*〉. In this paper, we study the

*p*-nilpotence of a group

*G*under the assumption that every subgroup of order

*d*of a Sylow

*p*-subgroup

*P*of

*G*with 1 <

*d*< |

*P*| is weakly

*ℌ*-embedded in

*G*. Many known results related to

*p*-nilpotence of a group

*G*are generalized.

## Abstract

Let *R* be a discrete valuation ring, *P* ∈*R*[*X*] a monic irreducible polynomial, and *K* the quotient field of *R*. We give in this paper a lower bound for the *P* over *R* in terms of the degrees of the monic irreducible factors of the reduction of *P* modulo *P* generates a power basis for the integral closure of R in the field extension of *K* defined by *P*.

## Abstract

In this article, we study the class of rings in which every regular locally principal ideal is projective called *LPP*-rings. We investigate the transfer of this property to various constructions such as direct products, amalgamation of rings, and trivial ring extensions. Our aim is to provide examples of new classes of commutative rings satisfying the above-mentioned property.

## Abstract

In this paper we study the uniform approximation of functions by a generalization of the Picard and Gauss-Weierstrass operators of max-product type in exponential weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity. We extend and improve previous results.

## Abstract

This paper deals with the existence and uniqueness of weak solution of a problem which involves a class of *A*-harmonic elliptic equations of nonhomogeneous type. Under appropriate assumptions on the function *f*, our main results are obtained by using Browder Theorem.

## Abstract

In this paper, we introduce a new three-parameter generalized version of the Gompertz model called the odd log-logistic Gompertz (OLLGo) distribution. It includes some well-known lifetime distributions such as Gompertz (Go) and odd log-logistic exponential (OLLE) as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the *k*th order moment, moment generating function and the quantile measure are provided. We discuss maximum likelihood estimation of the OLLGo parameters as well as three other estimation methods from one observed sample. The flexibility and usefulness of the new distribution is illustrated by means of application to a real data set.

## Abstract

Let *R* be an *IF* ring, or be a ring such that each right *R*-module has a monomorphic flat envelope and the class of flat modules is coresolving. We firstly give a characterization of copure projective and cotorsion modules by lifting and extension diagrams, which implies that the classes of copure projective and cotorsion modules have some balanced properties. Then, a relative right derived functor is introduced to investigate copure projective and cotorsion dimensions of modules. As applications, some new characterizations of *QF* rings, perfect rings and noetherian rings are given.

## Abstract

In 1971 Onnewer and Waterman establish a sufficient condition which guarantees uniform convergence of Vilenkin-Fourier series of continuous function. In this paper we consider different classes of functions of generalized bounded oscillation and in the terms of these classes there are established sufficient conditions for uniform convergence of Cesàro means of negative order.

## Abstract

In , a universal linear algebraic model was proposed for describing homogeneous conformal geometries, such as the spherical, Euclidean, hyperbolic, Minkowski, anti-de Sitter and Galilei planes (). This formalism was independent from the underlying field, providing an extension and general approach to other fields, such as finite fields. Some steps were taken even for the characteristic 2 case.

In this article, we undertake the study of the characteristic 2 case in more detail. In particular, the concept of virtual quadratic spaces is used (), and a similar result is achieved for finite fields of characteristic 2 as for other fields. Some differences from the non-characteristic 2 case are also pointed out.

## Abstract

In this note connections between root extensions of monoids and some finiteness conditions on monoids are studied, giving new proofs and generalizing results of Etingof, Malcolmson and Okoh for domains. In the same spirit, results of Jedrzejewicz and Zielinski on root-closed extensions of domains are generalized and sharpened to monoids. Using the same methods, a criterion for being a completely integrally closed domain is generalized to monoids.

## Abstract

In this paper first, we prove some new generalizations of Hermite-Hadamard type inequalities for the convex function *f* and for (*s, m*)-convex function *f* in the second sense in conformable fractional integral forms. Second, by using five new integral identities, we present some new Riemann-Liouville fractional trapezoid and midpoint type inequalities. Third, using these results, we present applications to *f*-divergence measures. At the end, some new bounds for special means of different positive real numbers and new error estimates for the trapezoidal and midpoint formula are provided as well. These results give us the generalizations of the earlier results.