Recursos de colección
Project Euclid (Hosted at Cornell University Library) (191.996 recursos)
Journal of Generalized Lie Theory and Applications
Journal of Generalized Lie Theory and Applications
Al Adeh, Fayez Fok
The aim of this paper is to prove the celebrated Riemann Hypothesis. I have already discovered a simple proof of the Riemann Hypothesis. The hypothesis states that the nontrivial zeros of the Riemann zeta function have real part equal to 0.5. I assume that any such zero is s=a+bi. I use integral calculus in the first part of the proof. In the second part I employ variational calculus. Through equations (50) to (59) I consider (a) as a fixed exponent, and verify that a=0.5. From equation (60) onward I view (a) as a parameter (a <0.5) and arrive at a...
Davis, S
The reduction of higher-dimensional theories over a coset space S/R is known to
yield a residual gauge symmetry related to the number of R-singlets in the
decomposition of S with respect to R. It is verified that this invariance is
identical to that found by requiring that there is a subgroup of the isometry
group with an action on the connection form that yields a transformation rule
defined only on the base space. The Lagrangian formulation of the projection of
the frame of global vector fields from S7 to the Lie group submanifold S3× S3 is
considered. The structure of an octonionic Chern-Simons gauge theory is
described.
Pereira, MA
This paper presents a simple and purely geometrical Grand Unification Theory.
Quantum Gravity, Electrostatic and Magnetic interactions are shown in a unified
framework. Newton’s Gravitational Law, Gauss’ Electrostatics Law and
Biot-Savart’s Electromagnetism Law are derived from first principles.
Gravitational Lensing, Mercury Perihelion Precession are replicated within the
theory. Unification symmetry is defined for all the existing forces. This
alternative model does not require Strong and Electroweak forces. A 4D
Shock-Wave Hyperspherical topology is proposed for the Universe which together
with a Quantum Lagrangian Principle and a Dilator based model for matter result
in a quantized stepwise expansion for the whole Universe along a radial
direction within a 4D spatial manifold....
Li, Juanjuan; Fan, Guangzhe
This paper is devoted to investigating the structure theory of a class of
not-finitely graded Lie superalgebras related to generalized super-Virasoro
algebras. In particular, we completely determine the derivation algebras, the
automorphism groups and the second cohomology groups of these Lie
superalgebras.
Nairn, Kris A
The moduli space for a flat G-bundle over the two-torus is completely determined
by its holonomy representation. When G is compact, connected, and simply
connected, we show that the moduli space is homeomorphic to a product of two
tori mod the action of the Weyl group, or equivalently to the conjugacy classes
of commuting pairs of elements in G. Since the component group for a non-simply
connected group is given by some finite dimensional subgroup in the centralizer
of an n-tuple, we use diagram automorphisms of the extended Dynkin diagram to
prove properties of centralizers of pairs of elements in G.
Shtukar, U
Famous K. Gauss introduced reduced row echelon forms for matrices approximately
200 years ago to solve systems of linear equations but the number of them and
their structure has been unknown until 2016 when it was determined at first in
the previous article given up to (n−1)×n matrices. The similar method is applied
to find reduced row echelon forms for (n−2)×n matrices in this article, and all
canonical bases for (n−2)-dimensional subspaces of -dimensional vector space are
found also.
Alexandre, C; Bordemann, M; Rivière, S; Wagemann, F
In this paper we focus on a certain self-distributive multiplication on
coalgebras, which leads to so-called rack bialgebra. Inspired by semi-group
theory (adapting the Suschkewitsch theorem), we do some structure theory for
rack bialgebras and cocommutative Hopf dialgebras. We also construct canonical
rack bialgebras (some kind of enveloping algebras) for any Leibniz algebra and
compare to the existing constructions. We are motivated by a differential
geometric procedure which we call the Serre functor: To a pointed differentible
manifold with multiplication is associated its distribution space supported in
the chosen point. For Lie groups, it is wellknown that this leads to the
universal enveloping algebra of the Lie algebra. For...
Shtukar, Uladzimir
Canonical bases for subspaces of a vector space are introduced as a new effective
method to analyze subalgebras of Lie algebras. This method generalizes well
known Gauss-Jordan elimination method.
Oyadare, OO
This paper reconsiders the age-long problem of normed linear spaces which do not
admit inner product and shows that, for some subspaces, Fn(G), of real
Lp(G)−spaces (when G is a reductive group in the Harish-Chandra class and p=2n),
the situation may be rectified, via an outlook which generalizes the fine
structure of the Hilbert space, L2(G). This success opens the door for harmonic
analysis of unitary representations, G→End(Fn(G)), of G on the
Hilbert-substructure Fn(G), which has hitherto been considered impossible.
Shtukar, Uladzimir
Canonical bases for (n-1)-dimensional subspaces of n-dimensional vector space are
introduced and classified in the article. This result is very prospective to
utilize canonical bases at all applications. For example, maximal subalgebras of
Lie algebras can be found using them.
Nazarkandi, HA
By considering a C∞ structure on the ordered non-increasing of elements of Rn, we
show that it is a differentiable manifold. By using of Lie groups, we show that
eigenvalue function is a submersion. This fact is used to prove some results.
These results is applied to prove a few facts about spectral manifolds and
spectral functions. Orthogonal matrices act on the real symmetric matrices as a
Lie transformation group. This fact, also, is used to prove the results.
Crooks, Peter
We consider aspects of the relationship between nilpotent orbits in a semisimple real Lie algebra $\mathfrak{g}$ and those in
its complexification $\mathfrak{g}_{\mathbb{C}}$. In particular, we prove that two distinct real nilpotent orbits lying in the same complex orbit are
incomparable in the closure order. Secondly, we characterize those $\mathfrak{g}$ having non-empty intersections with all nilpotent
orbits in $\mathfrak{g}_{\mathbb{C}}$. Finally, for $\mathfrak{g}$ quasi-split, we characterize those complex nilpotent orbits containing real ones.
Karpushkin , EV
The modern Science has now a lot of its branches and meanders, where are working the numerous specialists
and outstanding scientists everywhere in the whole world. The theme of this article is devoted to mathematics in
general and to such a new subsidiary science as the Cartesian infinitology (± ∞: x y and x y z) in a whole.
¶
The young and adult modern people of our time, among them, in first turn, are such ones as the usual citizens,
students or schoolchildren, have a very poor imagination about those achievements and successes that made by our
scientists in the different parts and divisions of...
Barna, IF; Kersner, R
Analytic solutions for cylindrical thermal waves in solid medium are given based on the nonlinear hyperbolic
system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law
is generalized where the relaxation time and heat propagation coefficient have a general power law temperature
dependence. From such laws one cannot form a second order parabolic or telegraph-type equation.We consider the
original non-linear hyperbolic system itself with the self-similar Ansatz for the temperature distribution and for the heat
flux. As results continuous.
Lantonirina, LS
Let Χ a diferentiable paracompact manifold. Under the hypothesis of a linear connection r with free torsion Τ on
Χ, we are going to give more explicit the proofs done by Vey for constructing a Riemannian structure. We proposed
three ways to reach our object. First, we give a sufficient and necessary condition on all of holonomy groups of the
connection ∇ to obtain Riemannian structure. Next, in the analytic case of $Χ$, the existence of a quadratic positive
definite form g on the tangent bundle ΤΧ such that it was invariant in the infinitesimal sense by the linear operators
∇$^k$R, where R is the...
Anona, FM
It emphasizes the mathematical aspects of the formation of sikidy. The sikidy as an art of divination is transmitted
by oral tradition, the knowledge of these mathematical relationships allows for a more consistent language of sikidy. In
particular, one can calculate systematically all ”into sikidy” special tables of Sikidy used in the ”ody” (kind of talismans).
Nikolaev, IV
It is proved that the Hilbert class field of a real quadratic field $Q(\sqrt{D})$ modulo a power $m$ of the conductor $f$ is
generated by the Fourier coefficients of the Hecke eigenform for a congruence subgroup of level $fD$.
Merger, J; Borzi, A
This work deals with an extension of the Black-Scholes model for rating options with the Heston volatility model.
A Lie-algebraic analysis of this equation is applied to reduce its order and compute some of its solutions. As a result
of this method, a five-parameter family of solutions is obtained. Though, these solutions do not match the terminal and
boundary conditions, they can be used for the validation of numerical schemes.
Ndoune, N; Bouetou Bouetou, T
In this paper, we introduce the notion of representation of Bol algebra. We prove an analogue of the classical
Engel’s theorem and the extension of Ado-Iwasawa theorem for Bol Algebras. We study the category of representations
of Bol algebras and show that it is a tensor category. In the case of regular representations of Bol algebras, we give
a complete classification of them for all two-dimensional Bol algebras.
Nadjafikhah, M; Pourrostami, N
In this paper, we prove that equation $E ≡ u_1-u_{_x2_t}+u_xf(u)-au_xu_{}x^2-buu_{x^3}=0$ is self-adjoint and quasi self-adjoint,
then we construct conservation laws for this equation using its symmetries. We investigate a symmetry classification
of this nonlinear third order partial differential equation, where $f$ is smooth function on $u$ and $a$, $b$ are arbitrary constans.
We find Three special cases of this equation, using the Lie group method.