scholarly journals On a new class of operators and Weyl type theorems

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 629-636 ◽  
Author(s):  
Salah Mecheri
Keyword(s):  
Present Article ◽  
Simple Pole ◽  
Open Problems ◽  
New Class ◽  
Paranormal Operator ◽  
Weyl Type Theorems ◽  
Isolated Point

In the present article, we introduce a new class of operators which will be called the class of k-quasi *-paranormal operators that includes '-paranormal operators. A part from other results, we show that following results hold for a k-quasi *-paranormal operator T: (i) T has the SVEP. (ii) Every non-zero isolated point in the spectrum of T is a simple pole of the resolvent of T. (iii) All Weyl type theorems hold for T. (iv) Comments and some open problems are also presented.

Biosimilars

2017 ◽  
pp. 171-188
Author(s):  
Anil K. Sharma ◽  
Raj K. Keservani ◽  
Rajesh K. Kesharwani
Keyword(s):  
Renal Failure ◽  
Present Article ◽  
Recombinant Dna ◽  
Recombinant Dna Technology ◽  
New Class ◽  
Patients With Diabetes ◽  
Dna Technology ◽  
Live Organism

Biosimilars are a new class of drugs, which are derived from live organism through the recombinant DNA technology. These are recently introduced in the pharmaceutical field for the preparation of drug to prevent or control the diseases. Patients with diabetes and renal failure may already be receiving biosimilar epoetin and may receive same insulin in coming years. The main aim of present article is to introduce the fundamentals of biologics and to explain how they are different and what these differences mean for pharmacists.

scholarly journals Fractons

2019 ◽  
Vol 10 (1) ◽  
pp. 295-313 ◽  
Author(s):  
Rahul M. Nandkishore ◽  
Michael Hermele
Keyword(s):  
Elasticity Theory ◽  
Quantum Dynamics ◽  
Hamiltonian Dynamics ◽  
Topological Order ◽  
Spin Liquids ◽  
Open Problems ◽  
New Class ◽  
Exactly Solvable ◽  
Lattice Spin Models ◽  
Restricted Mobility

Fracton phases constitute a new class of quantum state of matter. They are characterized by excitations that exhibit restricted mobility, being either immobile under local Hamiltonian dynamics or mobile only in certain directions. These phases do not wholly fit into any of the existing paradigms but connect to areas including glassy quantum dynamics, topological order, spin liquids, elasticity theory, quantum information theory, and gravity. We begin by discussing gapped fracton phases, which may be described using exactly solvable lattice spin models. We then introduce the framework of tensor gauge theory, which provides a powerful complementary perspective and allows us to access gapless fracton phases. We discuss the basic properties of gapless fracton phases and their connections to elasticity theory and gravity. We also discuss what is known about the dynamics and thermodynamics of fractons at nonzero density before concluding with a brief survey of some open problems.

scholarly journals Paranormal operators on Banach spaces

1980 ◽  
Vol 21 (2) ◽  
pp. 161-168 ◽  
Author(s):  
N.N. Chourasia ◽  
P.B. Ramanujan
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Weyl’S Theorem ◽  
Paranormal Operator ◽  
Isolated Point

In this note we show that a paranormal operator T on a Banach space satisfies Weyl's theorem. This is accomplished by showing that(i) every isolated point of its spectrum is an eigenvalue and the corresponding eigenspace has invariant complement,(ii) for α ≠ 0, Ker(T-α) ⊥ Ker (T-β) (in the sense of Birkhoff) whenever β ≠ α.

scholarly journals Explicit formula of a new class of q-Hermite-based Apostol-type polynomials and generalization

2020 ◽  
Vol 26 (4) ◽  
pp. 93-102
Author(s):  
Mouloud Goubi ◽  
Keyword(s):  
Explicit Formula ◽  
Present Article ◽  
Generating Function ◽  
New Class

The present article deals with a recent study of a new class of q-Hermite-based Apostol-type polynomials introduced by Waseem A. Khan and Divesh Srivastava. We give their explicit formula and study a generalized class depending in any q-analog generating function.

scholarly journals Ergative diagnostics: temptatio redux

2003 ◽  
Vol 13 (1) ◽  
Author(s):  
Werner Abraham
Keyword(s):  
Present Article ◽  
Direct Object ◽  
Empirical Basis ◽  
New Class ◽  
The Past ◽  
Traditional Notion

In the past 20 years, a new class of verbs has seen the light of existence: 'unaccusative' or 'ergative' verbs. These verbs are intransitive, but different from the traditional notion of intransitive to the extent that their subject valency behaves like a direct object distributionally. Ever since the introduction of this new grammatical notion in (typologically non-ergative, i.e., accusative) languages like English a vast bulk of literature on this topic has come forth. The present article takes issue with this mainly Anglophil notion of unaccusativity/ergativity. The claim is that this notion does not make sense in languages which provide aspectual or aktionsart distinctions of perfectivity. 'Unaccusatives' are intransitive perfectives. This argument is carried through primarily on the empirical basis of German.

scholarly journals A Note on q -Fubini-Appell Polynomials and Related Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Abdulghani Muhyi ◽  
Serkan Araci
Keyword(s):  
Present Article ◽  
Generating Functions ◽  
Appell Polynomials ◽  
New Class ◽  
Special Polynomials ◽  
Series Representations ◽  
Polynomial Family

The present article is aimed at introducing and investigating a new class of q -hybrid special polynomials, namely, q -Fubini-Appell polynomials. The generating functions, series representations, and certain other significant relations and identities of this class are established. Some members of q -Fubini-Appell polynomial family are investigated, and some properties of these members are obtained. Further, the class of 3-variable q -Fubini-Appell polynomials is also introduced, and some formulae related to this class are obtained. In addition, the determinant representations for these classes are established.

scholarly journals On a new class of fractional partial differential equations II

2018 ◽  
Vol 11 (3) ◽  
pp. 289-307 ◽  
Author(s):  
Tien-Tsan Shieh ◽  
Daniel E. Spector
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Partial Differential Equations ◽  
Lagrange Equations ◽  
Partial Differential ◽  
Open Problems ◽  
New Class ◽  
Existence Of Minimizers ◽  
Fractional Pde ◽  
Regularity Results

AbstractIn this paper we continue to advance the theory regarding the Riesz fractional gradient in the calculus of variations and fractional partial differential equations begun in an earlier work of the same name. In particular, we here establish an {L^{1}} Hardy inequality, obtain further regularity results for solutions of certain fractional PDE, demonstrate the existence of minimizers for integral functionals of the fractional gradient with non-linear dependence in the field, and also establish the existence of solutions to corresponding Euler–Lagrange equations obtained as conditions of minimality. In addition, we pose a number of open problems, the answers to which would fill in some gaps in the theory as well as to establish connections with more classical areas of study, including interpolation and the theory of Dirichlet forms.

scholarly journals Some Fixed Point Results in b-Metric Spaces and b-Metric-Like Spaces with New Contractive Mappings

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 55
Author(s):  
Kapil Jain ◽  
Jatinderdeep Kaur
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Linear Equations ◽  
Open Problems ◽  
New Class ◽  
Contractive Mappings ◽  
Simultaneous Linear Equations ◽  
Class Of Functions

The aim of our paper is to present a new class of functions and to define some new contractive mappings in b-metric spaces. We establish some fixed point results for these new contractive mappings in b-metric spaces. Furthermore, we extend our main result in the framework of b-metric-like spaces. Some consequences of main results are also deduced. We present some examples to illustrate and support our results. We provide an application to solve simultaneous linear equations. In addition, we present some open problems.

Fuzzy Θf-contractive mappings and their fixed points with applications

2020 ◽  
Vol 39 (5) ◽  
pp. 7097-7106
Author(s):  
Hayel Nasr Saleh ◽  
Mohammad Imdad ◽  
Idrees Khan ◽  
Md Hasanuzzaman
Keyword(s):  
Dynamic Programming ◽  
Fixed Point ◽  
Fixed Points ◽  
Present Article ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Auxiliary Function ◽  
Fuzzy Metric Spaces ◽  
New Class ◽  
Contractive Mappings

In the present article, inspired by the work of Jleli et al. [J. Inequal. Appl. 2014, 38 (2014)] and [J. Inequal. Appl. 2014, 439 (2014)] in metric spaces, we proposed a new class of contractive mappings termed as: fuzzy Θf-contractive mappings by using an auxiliary function Θf : (0, 1) → (0, 1) satisfying suitable properties. This class has further been weakened by defining the class of fuzzy Θf-weak contractive mappings to realize yet another class of contractive mappings. Thereafter, these two newly introduced classes of contractive mappings are utilized to establish some fixed point theorems in M-complete fuzzy metric spaces (in the sense of George and Veeramani). In support of our newly obtained results, we provide some examples besides furnishing applications to dynamic programming.

Elementary completeness properties of intuitionistic logic with a note on negations of prenex formulae

1958 ◽  
Vol 23 (3) ◽  
pp. 317-330 ◽  
Author(s):  
G. Kreisel
Keyword(s):  
Present Article ◽  
Intuitionistic Logic ◽  
Classical Logic ◽  
Predicate Logic ◽  
Formal Proof ◽  
Predicate Calculus ◽  
Open Problems

The purpose of the present article is to formulate in an intuitionistically meaningful manner the completeness problems for the intuitionistic predicate calculus, and to establish the completeness of certain fragments of it. In these proofs certain translations of classical logic into intuitionistic logic are used, in particular those discovered by Kolmogorov [11] and Gödel [3], and a new one in which negations of prenex formulae are central. Since the last one is of interest also independently of the completeness problems, the details are presented separately at the end of this paper.All arguments are intended to be intuitionistically valid unless the opposite is stated; in particular, ‘proof’ means intuitionistic proof, and ‘formal proof’ means proof in the relevant system of Heyting [4], [5].Open problems are mentioned in Remarks 3.1 and 8.1.German capitals denote formulae of predicate logic, Latin (italic) capitals denote predicate symbols or propositional letters.

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