Differential Identities Research Articles

Some commutativity criteria for prime rings with differential identities on Jordan ideals

In this article, we present some commutativity theorems for a ring R equipped with a generalized derivation satisfying certain differential identities on Jordan ideals of R. Some related results for prime rings are also discussed. Finally; we provide examples to show that the assumed restrictions are not superfluous.

Commutativity of near-rings with certain constrains on Jordan ideals

The purpose of this paper is to study derivations satisfying certain differential identities on Jordan ideals of 3-prime near-rings. Moreover, we provide examples to show that hypothesis of our results are necessary.

Energy content in linear mechanical systems with arbitrary time dependence

A novel complementary variables formulation, permits the obtainment of invariants of a mechanical system following the rationale of Abel's differential equation identity. This approach allows for the decomposition of the total energy of the system into the energy of the object and the dynamic energy of the field. The force acting on the object must be linear in the spatial variable but is arbitrary in the time variable. Several examples, such as the time dependent harmonic oscillator and a swing are described with this complementary variables formulation. The exact solution for the energy of a Lorentz pendulum with uniformly varying length is presented.

Differential identities on prime rings with involution

In this paper, we investigate commutativity of prime rings [Formula: see text] with involution ∗ of the second kind in which generalized derivations satisfy certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Furthermore, we provide an example to show that the restriction imposed on the involution is not superfluous.

On the equations of electrodynamics in a flat or curved spacetime and a possible interaction energy

AbstractIn this paper the independent equations of continuum electrodynamics and their quantity are investigated, beginning with the standard equations used in special and general relativity. Using differential identities it is checked that there are as many independent equations as there are unknowns, for the case with given sources as well as for the general case where the motion of the charged medium producing the field is unknown. This problem is then discussed in an alternative theory of gravity with a preferred reference frame, in order to constrain an additional, “interaction” energy tensor that has to be postulated in this theory, and that would be present also outside usual matter. In order that the interaction tensor be Lorentz-invariant in special relativity, it has to depend only on a scalar fieldp. Since the system of electrodynamics is closed in the absence of the interaction tensor, just one scalar equation more is needed to close it again in the presence ofp. That equation is taken to be the equation for charge conservation. Finally, the equations that allow the determination of fieldpare derived in a given weak gravitational field and in a given electromagnetic field.

Attitudes towards Personhood in the Locked-in Syndrome: from Third- to First- Person Perspective and to Interpersonal Significance

Personhood is ascribed on others, such that someone who is recognized to be a person is bestowed with certain civil rights and the right to decision making. A rising question is how severely brain-injured patients who regain consciousness can also regain their personhood. The case of patients with locked-in syndrome (LIS) is illustrative in this matter. Upon restoration of consciousness, patients with LIS find themselves in a state of profound demolition of their bodily functions. From the third-person perspective, it can be expected that LIS patients might experience a differential personal identity and may lose their status as persons. However, from the patients’ perspective, it is uncontested that they retain their personal identity and that they consider themselves to be persons. We here include results from a survey with patients with LIS aimed at identifying the primary expectations of patients for their care by non-medical professionals. Based on these first-hand reports, we argue that personhood in LIS is progressively regained as the widening circle of others recognizes them as persons.

Differential identities, 2 × 2 upper triangular matrices and varieties of almost polynomial growth

We study the differential identities of the algebra UT2 of 2×2 upper triangular matrices over a field of characteristic zero. We let the Lie algebra L=Der(UT2) of derivations of UT2 (and its universal enveloping algebra) act on it. We study the space of multilinear differential identities in n variables as a module for the symmetric group Sn and we determine the decomposition of the corresponding character into irreducibles.If V is the variety of differential algebras generated by UT2, we prove that unlike the other cases (ordinary identities, group graded identities) V does not have almost polynomial growth. Nevertheless we exhibit a subvariety U of V having almost polynomial growth.

Some differential identities on prime and semiprime rings and Banach algebras

In this manuscript, we discuss the behaviour and nature of generalized derivation \({\mathscr {G}}\) on a (semi-) prime ring \({\mathscr {R}}\) satisfying certain differential identities over \({\mathscr {I}}\), a nonzero ideal of \({\mathscr {R}}\). Moreover, we extend our purely ring theoretic result to a non-commutative Banach algebras and obtained some range inclusion results of continuous generalized derivations.

Phase space methods for Majorana fermions

Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The resulting phase-space of covariance matrices belongs to the symmetry class D, one of the non-standard symmetry classes. This was originally proposed to study mesoscopic normal-metal-superconducting hybrid structures, which is the type of structure that has led to recent experimental observations of Majorana fermions. Under a unitary transformation, it is possible to express these Gaussian operators using real anti-symmetric matrices and Majorana operators, which are much simpler mathematical objects. We derive differential identities involving Majorana fermion operators and an antisymmetric matrix which are relevant to the derivation of the corresponding Fokker–Planck equations on symmetric space. These enable stochastic simulations either in real or imaginary time. This formalism has direct relevance to the study of fermionic systems in which there are Majorana type excitations, and is an alternative to using expansions involving conventional Fermi operators. The approach is illustrated by showing how a linear coupled Hamiltonian as used to study topological excitations can be transformed to Fokker–Planck and stochastic equation form, including dissipation through particle losses.

Generalized Derivations on Prime Rings with Involution

Let \(R\) be an associative ring. An additive mapping \(F : R \to R\) is called a generalized derivation with an associated derivation \(d\) of \(R\) if it satisfies \(F(xy) = F(x)y + xd(y)\) for all \(x, y \in R\). In the present paper, we obtain description of the structure of \(R\) and information about the generalized derivation \(F\) which satisfies certain \(\ast\)-differential identities on prime rings with involution.

Thermodynamic bounds for existence of normal shock in compressible fluid flow in pipes.

The present paper is concerned with the thermodynamic theory of the normal shock in compressible fluid flow in pipes, in the lights of the pioneering works of Lord Rayleigh and G. Fanno. The theory of normal shock in pipes is currently presented in terms of the Rayleigh and Fanno curves, which are shown to cross each other in two points, one corresponding to a subsonic flow and the other corresponding to a supersonic flow. It is proposed in this paper a novel differential identity, which relates the energy flux density, the linear momentum flux density, and the entropy, for constant mass flow density. The identity so obtained is used to establish a theorem, which shows that Rayleigh and Fanno curves become tangent to each other at a single sonic point. At the sonic point the entropy reaches a maximum, either as a function of the pressure and the energy density flux or as a function of the pressure and the linear momentum density flux. A Second Law analysis is also presented, which is fully independent of the Second Law analysis based on the Rankine-Hugoniot adiabatic carried out by Landau and Lifshitz (1959).

A quadratic differential identity with skew derivations

ABSTRACTLet R be a prime ring of characteristic different from 2, with right Martindale quotient ring Qr and extended centroid C, and let be a multilinear polynomial over C, not central valued on R. Suppose that F and G are skew derivations of R, associated with the automorphism α, such thatfor all . Then either F = 0 or G = 0.

Ku Klux Kasserole and Strange Fruit Pies: A Shouting Match at the Border in Cyberspace

Abstract Twitter users’ responses to the 2013 Paula Deen “N-word” scandal offer a rich site for examining how racial dynamics shape collective performances in digital spaces. Focusing on the tweets inspired by the #PaulasBestDishes hashtag, this article first shows how these vernacular forms of expression playfully engaged with Deen’s image system in order to speak back to the broader cultural discourses around racism in the present day. Second, it examines how the complex racial dynamics in the United States informed not only the content, but also the social context of these tweets, attending specifically to how differential identity served as the social base of this collective digital performance. Ultimately, this article identifies new avenues of inquiry for gaining a greater understanding of the dynamics of digital performance within a cultural context shaped by social difference and ongoing racial tensions.

Differential identity of Filopodia and Tunneling Nanotubes revealed by the opposite functions of actin regulatory complexes.

Tunneling Nanotubes (TNTs) are actin enriched filopodia-like protrusions that play a pivotal role in long-range intercellular communication. Different pathogens use TNT-like structures as “freeways” to propagate across cells. TNTs are also implicated in cancer and neurodegenerative diseases, making them promising therapeutic targets. Understanding the mechanism of their formation, and their relation with filopodia is of fundamental importance to uncover their physiological function, particularly since filopodia, differently from TNTs, are not able to mediate transfer of cargo between distant cells. Here we studied different regulatory complexes of actin, which play a role in the formation of both these structures. We demonstrate that the filopodia-promoting CDC42/IRSp53/VASP network negatively regulates TNT formation and impairs TNT-mediated intercellular vesicle transfer. Conversely, elevation of Eps8, an actin regulatory protein that inhibits the extension of filopodia in neurons, increases TNT formation. Notably, Eps8-mediated TNT induction requires Eps8 bundling but not its capping activity. Thus, despite their structural similarities, filopodia and TNTs form through distinct molecular mechanisms. Our results further suggest that a switch in the molecular composition in common actin regulatory complexes is critical in driving the formation of either type of membrane protrusion.

Two sided $\alpha $-derivations in 3-prime near-rings

The purpose of this paper is to investigate two sided $\alpha $-derivations satisfying certain differential identities on 3-prime near-rings. Some well-known results characterizing commutativity of 3-prime near-rings by derivations (semi-derivations) have been generalized. Furthermore, examples proving the necessity of the 3-primeness hypothesis are given.

ON SEMIDERIVATIONS IN 3-PRIME NEAR-RINGS

In the present paper, we expand the domain of work on the concept of semiderivations in 3-prime near-rings through the study of structure and commutativity of near-rings admitting semiderivations satisfying certain differential identities. Moreover, several examples have been provided at places which show that the assumptions in the hypotheses of various theorems are not altogether superfluous.

Nonlinear identities with skew derivations

Let R be a prime ring with the extended centroid c. Suppose that R is acted by a pointed coalgebra with group-like elements acting as automorphisms of R. A generalized polynomial with variables acted by the coalgebra is called an identity if it vanishes on R. We prove the following:(1) If c is a perfect field, then any such identity is a consequence of simple basic identities defined in [6] and GPIs of R with variables acted by Frobenius automorphisms.(2) If c is not a perfect field, then any such identity is a consequence of simple basic identities defined in [6] and GPIs of R.With this, we extend Yanai's result [25] to “nonlinear identities”. These are actually special instances of our Theorems 1 and 2 below respectively, which extend Kharchenko's theory of differential identities [14,15] to the context of expansion closed word sets introduced in [6].

Differential Identities for Nonlinear Partial Differential Equations

We obtain new algebraic analytic presentations for solutions and coefficients of nonlinear second order differential equations and systems of such equations. Bibliography: 18 titles.

A Female Identity Switch Helps Keep Only One Egg in the Basket

The flowering plant female gametophyte carries two gametes, an egg cell and a central cell, whose double fertilization gives rise to embryo and endosperm, respectively. In this issue of Developmental Cell, Yuan et al. (2016) identify the protein CKI1 as a key switch that controls the differential female gamete identities.

Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

The importance of Einstein’s geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified. The use of Bianchi identity to write the field equations of GR is shown. Another similar identity in the absolute parallelism geometry is given. A more general differential identity in the parameterized absolute parallelism geometry is derived. Comparison and interrelationships between the above mentioned identities and their role in constructing field theories are discussed.