scholarly journals Inhomogeneous Partition Regularity

10.37236/7972 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Imre Leader ◽  
Paul A. Russell
Keyword(s):  
Commutative Ring ◽  
Direct Proof ◽  
Integer Vector ◽  
System Of Equations ◽  
Main Ingredient ◽  
Integer Matrix ◽  
Constant Solution

We say that the system of equations $Ax = b$, where $A$ is an integer matrix and $b$ is a (non-zero) integer vector, is partition regular if whenever the integers are finitely coloured there is a monochromatic vector $x$ with $Ax = b.$ Rado proved that the system $Ax = b$ is partition regular if and only if it has a constant solution. Byszewski and Krawczyk asked if this remains true when the integers are replaced by a general (commutative) ring $R$. Our aim in this note is to answer this question in the affirmative. The main ingredient is a new 'direct' proof of Rado’s result.

scholarly journals Properties of the aggregated quasi-hydrodynamic system of equations for a homogeneous gas mixture with a common regularizing velocity

2021 ◽  
pp. 1-26
Author(s):  
Alexander Anatolievich Zlotnik ◽  
Anna Sergeevna Fedchenko
Keyword(s):  
Original System ◽  
New Technique ◽  
Gas Mixture ◽  
System Of Equations ◽  
Symmetric Form ◽  
Hydrodynamic System ◽  
Constant Solution ◽  
Multicomponent Gas ◽  
A New Technique ◽  
Multicomponent Gas Mixture

We study a quasi-hydrodynamic system of equations for a homogeneous (with common velocity and temperature) multicomponent gas mixture in the absence of chemical reactions, with a regularizing velocity common for the components. We derive the entropy balance equation with a non-negative entropy production taking into account the diffusion fluxes of the mixture components. In the absence of diffusion fluxes, a system of equations linearized at a constant solution is constructed by a new technique, In the absence of diffusion fluxes, a system of equations linearized on a constant solution is constructed by a new technique. It is reduced to a symmetric form, the L^2-dissipativity of its solutions is proved, and a degeneration (with respect to the densities of the mixture components) of the parabolicity property for the original system is established. Actually, the system has the composite type. The obtained properties strictly reflect its physical correctness and dissipative nature of the quasi-hydrodynamic regularization.

scholarly journals The Smith normal form distribution of a random integer matrix

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Yinghui Wang ◽  
Richard P. Stanley
Keyword(s):  
Normal Form ◽  
Positive Integer ◽  
Smith Normal Form ◽  
Integer Vector ◽  
Integer Matrix ◽  
Random Integer ◽  
International Audience ◽  
Greatest Common Divisors

International audience We show that the density μ of the Smith normal form (SNF) of a random integer matrix exists and equals a product of densities μps of SNF over Z/psZ with p a prime and s some positive integer. Our approach is to connect the SNF of a matrix with the greatest common divisors (gcds) of certain polynomials of matrix entries, and develop the theory of multi-gcd distribution of polynomial values at a random integer vector. We also derive a formula for μps and determine the density μ for several interesting types of sets.

scholarly journals Coleman–Gross height pairings and the p-adic sigma function

2015 ◽  
Vol 2015 (698) ◽  
Author(s):  
Jennifer S. Balakrishnan ◽  
Amnon Besser
Keyword(s):  
Elliptic Curves ◽  
Direct Proof ◽  
Main Ingredient ◽  
Disjoint Support ◽  
Sigma Function

AbstractWe give a direct proof that the Mazur–Tate and Coleman–Gross heights on elliptic curves coincide. The main ingredient is to extend the Coleman–Gross height to the case of divisors with non-disjoint support and, doing some

Convergent-bceam diffraction studies on lead zirconate titanate Ceramics

1986 ◽  
Vol 44 ◽  
pp. 482-483
Author(s):  
M.L.A. Dass ◽  
T.A. Bielicki ◽  
G. Thomas ◽  
T. Yamamoto ◽  
K. Okazaki
Keyword(s):  
Lead Zirconate Titanate ◽  
Direct Proof ◽  
Lead Zirconate ◽  
Subsolidus Phase ◽  
Pzt Ceramics ◽  
Subsolidus Phase Diagram ◽  
Zirconate Titanate ◽  
Two Phases ◽  
Cbd Method ◽  
Titanate Ceramics

Lead zirconate titanate, Pb(Zr,Ti)O3 (PZT), ceramics are ferroelectrics formed as solid solutions between ferroelectric PbTiO3 and ant iferroelectric PbZrO3. The subsolidus phase diagram is shown in figure 1. PZT transforms between the Ti-rich tetragonal (T) and the Zr-rich rhombohedral (R) phases at a composition which is nearly independent of temperature. This phenomenon is called morphotropism, and the boundary between the two phases is known as the morphotropic phase boundary (MPB). The excellent piezoelectric and dielectric properties occurring at this composition are believed to.be due to the coexistence of T and R phases, which results in easy poling (i.e. orientation of individual grain polarizations in the direction of an applied electric field). However, there is little direct proof of the coexistence of the two phases at the MPB, possibly because of the difficulty of distinguishing between them. In this investigation a CBD method was found which would successfully differentiate between the phases, and this was applied to confirm the coexistence of the two phases.

Canonical Submersion and Lie Homomorphisms Normal Subgroup

2020 ◽  
Vol 23 (1) ◽  
pp. 97-101
Author(s):  
Mikhail Petrichenko ◽  
Dmitry W. Serow
Keyword(s):  
Normal Subgroup ◽  
Canonical System ◽  
System Of Equations ◽  
Core Group ◽  
The Core ◽  
Switch Group

Normal subgroup module f (module over the ring F = [ f ] 1; 2-diffeomorphisms) coincides with the kernel Ker Lf derivations along the field. The core consists of the trivial homomorphism (integrals of the system v = x = f (t; x )) and bundles with zero switch group Lf , obtained from the condition ᐁ( ω × f ) = 0. There is the analog of the Liouville for trivial immersion. In this case, the core group Lf derivations along the field replenished elements V ( z ), such that ᐁz = ω × f. Hence, the core group Lf updated elements helicoid (spiral) bundles, in particular, such that f = ᐁU. System as an example Crocco shown that the canonical system does not permit the trivial embedding: the canonical system of equations are the closure of the class of systems that permit a submersion.

LIQUIDUS THERMO-BAROMETER FOR THE MODELING OF MAGNETITE — MELT EQUILIBRIUM

2018 ◽  
pp. 71-80
Author(s):  
N. S. Aryaeva ◽  
E. V. Koptev-Dvornikov ◽  
D. A. Bychkov
Keyword(s):  
Experimental Data ◽  
Liquidus Temperature ◽  
Vertical Structure ◽  
Maximum Error ◽  
Silicate Melt ◽  
System Of Equations ◽  
Wide Range ◽  
Basaltic Melts ◽  
Multidimensional Statistics

A system of equations of thermobarometer for magnetite-silicate melt equilibrium was obtained by method of multidimensional statistics of 93 experimental data of a magnetite solubility in basaltic melts. Equations reproduce experimental data in a wide range of basalt compositions, temperatures and pressures with small errors. Verification of thermobarometers showed the maximum error in liquidus temperature reproducing does not exceed ±7 °C. The level of cumulative magnetite appearance in the vertical structure of Tsypringa, Kivakka, Burakovsky intrusions predicted with errors from ±10 to ±50 m.

THE HEXOSAMINE CONTENT OF THE ORBIT IN RELATION TO ANTI-THYROTROPHIN ANTIBODY TITRES IN SERA OF THYROTROPHIN-TREATED RABBITS WITH AND WITHOUT CORTISONE ADMINISTRATION

1962 ◽  
Vol 41 (3) ◽  
pp. 474-480 ◽  
Author(s):  
Otto Wegelius ◽  
E. J. Jokinen
Keyword(s):  
Connective Tissue ◽  
Guinea Pigs ◽  
Antibody Formation ◽  
Direct Proof ◽  
Significant Rise ◽  
Extraocular Muscles ◽  
Concomitant Treatment ◽  
Antibody Titres ◽  
Hexosamine Content ◽  
Synergetic Action

ABSTRACT In all previous investigations on experimental exophthalmos, heterologous thyrotrophic pituitary extracts have been used. These protein hormones stimulate antihormone formation in the test animals. Cortisone has been reported to effectively block antibody formation. In addition, it has been shown to potentiate TSH-induced exophthalmos in guinea-pigs. With rabbits as test animals, the hexosamine content of the orbital tissues was determined and used as an index of exophthalmos development and at the same time the antibody titres in the sera were followed. TSH injections for six weeks led to a highly significant accumulation of hexosamine in the retrobulbar connective tissue and in the extraocular muscles, i. e. an increase of up to 400% as compared with the control animals. At the same time a significant rise in antihormonal titres was detectable in the sera. Concomitant treatment with cortisone brought about an equal or higher accumulation of hexosamine but significantly lower antibody titres. The known opposite peripheral actions of TSH and cortisone can be reconciled with the synergy in producing experimental exophthalmos by attributing the synergetic action of cortisone to the blocking of antihormone formation. If less antihormones are produced, the effect of TSH is enhanced. Our experiments do not provide direct proof for this hypothesis. High hexosamine values in the orbit and low antihormone titres in the serum are, however, concomitant phenomena.

Study on the Modes of Operation of a Multi-Machine Installations with Mechanical Reduction

2019 ◽  
pp. 12-22
Author(s):  
A. M. Oleynikov ◽  
L. N. Kanov
Keyword(s):  
Mathematical Description ◽  
Reactive Power ◽  
Maximum Efficiency ◽  
Wind Flow ◽  
System Of Equations ◽  
Mechanical Equilibrium ◽  
Synchronous Generators ◽  
Electromagnetic Excitation ◽  
Number Of Generators ◽  
Wide Range

The paper gives the description of the original wind electrical installation with mechanical reduction in which the output of vertical axis wind turbine with rather low rotation speed over multiplicator is distributed to a certain number of generators. The number of acting generators is determined by the output of actual operating wind stream at each moment. According to this constructive scheme, it is possible to provide effective and with maximum efficiency installation work in a wide range of wind speeds and under any schedule issued to the consumer of electricity. As there are no any experience in using such complexes, mathematical description of its main elements is given, namely windwheels, generators with electromagnetic excitation of magnetic electrical type, then their interaction with windwheel, and also the results of mathematical modeling of work system regimes under using the offered system of equations. The basis for the mathematical description of the main elements of the installation – synchronous generators – are the system of equations of electrical and mechanical equilibrium in relative units in rotating coordinates without considering saturation of the magnetic circuit. The equation of mechanical equilibrium systems includes torque and brake windwheel electromagnetic moments of generators with taking into account the reduction coefficients and friction. In addition, we specify the alternator rotor dynamics resulting from continuous torque of windwheel fluctuations under the influence of unsteady wind flow and wind speed serving as the original variable is modeled by a set of sinusoids. Model simplification is achieved by equivalization of similar generators and by disregarding these transitions with a small time constant. Calculation the installation with synchronous generators of two types of small and medium capacity taking into account the operational factors allowed us to demonstrate the logic of interactions in the main elements of the reported complex in the process of converting wind flow into the generated active and reactive power. We have shown the possibility of stable system work under changeable wind stream condition by regulating of the plant blade angle and with simultaneous varying of generator number of different types. All these are in great interest for project organizations and power producers.

On quasi-radical of near-ring of polynomials

2019 ◽  
Vol 56 (2) ◽  
pp. 252-259
Author(s):  
Ebrahim Hashemi ◽  
Fatemeh Shokuhifar ◽  
Abdollah Alhevaz
Keyword(s):  
Commutative Ring ◽  
Nilpotent Elements ◽  
Ring Of Polynomials

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 R0[x] equals to the set of all nilpotent elements of R0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R0[x] is a subset of the intersection of all maximal left ideals of R0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R0[x] coincides with the intersection of all maximal left ideals of R0[x]. Moreover, we prove that the quasi-radical of R0[x] is the greatest quasi-regular (right) ideal of it.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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