Inertial law of symplectic forms on modules over plural algebra

Marek Jukl

Displaying similar documents to “Inertial law of symplectic forms on modules over plural algebra”

Remarks on generalized solutions of ordinary linear differential equations in the Colombeau algebra

Jan Ligęza (1998)

Mathematica Bohemica

Similarity:

In this paper first order linear ordinary differential equations are considered. It is shown that the Cauchy problem for these systems has a unique solution in $𝒢^{n} (ℝ)$ , where $𝒢 (ℝ)$ denotes the Colombeau algebra.

Spectral properties of fourth order differential operators

Ondřej Došlý, Roman Hilscher (1997)

Mathematica Bohemica

Similarity:

Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator $ℓ (y) \equiv \frac{1}{w (t)} (r (t) y)$ , $t \in [a, \infty)$ are established. These conditions are based on a recently proved relationship between spectral properties of $ℓ$ and oscillation of a certain associated second order differential equation.

Reflected double layer potentials and Cauchy's operators

Dagmar Medková (1998)

Mathematica Bohemica

Similarity:

Necessary and sufficient conditions are given for the reflected Cauchy's operator (the reflected double layer potential operator) to be continuous as an operator from the space of all continuous functions on the boundary of the investigated domain to the space of all holomorphic functions on this domain (to the space of all harmonic functions on this domain) equipped with the topology of locally uniform convergence.

On systems of linear algebraic equations in the Colombeau algebra

Jan Ligęza, Milan Tvrdý (1999)

Mathematica Bohemica

Similarity:

From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra $\bar{ℝ}$ of generalized real numbers. It is worth mentioning that the algebra $\bar{ℝ}$ is not a field.

Comparison theorems for differential equations of neutral type

Miroslava Růžičková (1997)

Mathematica Bohemica

Similarity:

We are interested in comparing the oscillatory and asymptotic properties of the equations $L_{n} [x (t) - P (t) x (g (t))] + δ f (t, x (h (t))) = 0$ with those of the equations $M_{n} [x (t) - P (t) x (g (t))] + δ Q (t) q (x (r (t))) = 0 .$

Transitivity and partial order

Jiří Klaška (1997)

Mathematica Bohemica

Similarity:

In this paper we find a one-to-one correspondence between transitive relations and partial orders. On the basis of this correspondence we deduce the recurrence formula for enumeration of their numbers. We also determine the number of all transitive relations on an arbitrary $n$ -element set up to $n = 14$ .