Group Analysis of the Plane Steady Vortex Submodel of Ideal Gas with Varying Entropy

The submodel of ideal gas motion being invariant with respect to the time translation and the space translation by one direct has 4 integrals in the case of vortex flows with the varying entropy. The system of nonlinear differential equations of the third order with one arbitrary element was obtained for a stream function and a specific volume. This element contains from the state equation and arbitrary functions of the integrals. The equivalent transformations were found for arbitrary element. The problem of the group classification was solved when admitted algebra was expanded for 8 cases of arbitrary element. The optimal systems of dissimilar subalgebras were obtained for the Lie algebras from the group classification. The example of the invariant vortex motion from the point source or sink was done. The regular partial invariant submodel was considered for the 2-dimensional subalgebra. It describes the turn of a vortex flow in the strip and on the plane with asymptotes for the stream line.

On essential elements in a lattice and Goldie analogue theorem

We introduce the concept of essentiality in a lattice [Formula: see text] with respect to an element [Formula: see text]. We define notions such as [Formula: see text]-essential, [Formula: see text]-uniform elements and obtain some of their properties. Examples of lattices are given wherein essentiality can be retained with respect to an arbitrary element (specifically, there are elements in [Formula: see text] which are [Formula: see text]-essential but not essential). We prove Goldie analogue results in terms of [Formula: see text]-uniform elements and [Formula: see text]-∨-independent sets. Furthermore, we define a graph with respect to [Formula: see text]-essential element in a lattice and study its properties.

Relations on topologized groups

: In our present paper, topological groups are being discussed, where the relations with counter examples built the interest in the generalized structure. Some of these structures have also been converted into the other structures using topological isomorphism. In our work, the identity element plays the important role in lieu of arbitrary element. The role of topology has the more interest in our discipline.

Reflecții asupra conceptului de artă obiectivă în contextul artei contemporane

"Reflections on the concept of objective art in the context of contemporary art. Objective art communicates about the human being and his/her place in the universe, about the cosmic laws and the role they play in human life and provide clues as to how man can relate to them. From literary sources attesting to the idea that art in its origin had the role of transmitting knowledge to future generations, we deduce that in ancient times all art forms could be read like a book, and those who knew how to read, fully understood the meaning of the knowledge that was incorporated in these art forms. Nevertheless, there are two forms of art, one very different from the other: objective art and subjective art. Everything that we call art today is subjective art. Objective art is the authentic work resulted from the deliberate, premeditated efforts of a conscious artist. In the act of his creation, the artist avoids or eliminates any subjective or arbitrary element and the impression that such a work evokes in others is always defined. Keywords: objective art, the art of antiquity, contemporary art "

Properties of the commutators of some elements of linear groups over divisions rings

Inclusions resulting from the commutativity of elements and their commutators with trans\-vections in the language of residual and fixed submodules are found. The residual and fixed submodules of an element $\sigma $ of the complete linear group are defined as the image and the kernel of the element $\sigma -1$ and are denoted by $R(\sigma )$ and $P(\sigma )$, respectively. It is shown that for an arbitrary element $g$ of a complete linear group over a division ring whose characteristic is different from 2 and the transvection $\tau $ from the commutativity of the commutator $\left[g,\tau \right]$ with $g$ is followed by the inclusion of $R(\left[g,\tau \right])\subseteq P(\tau )\cap P(g)$. It is proved that the same inclusions occur over an arbitrary division ring if $g$ is a unipotent element, $\mathrm{dim}\mathrm{}(R\left(\tau \right)+R\left(g\right))\le 2$ and the commutator $\left[g,\tau \right]$ commutes with $\tau $ or if $g$ is a unipotent commutator of some element of the complete linear group and transvection $\ \tau $.

ETA-RULES IN MARTIN-LÖF TYPE THEORY

The eta rule for a set A says that an arbitrary element of A is judgementally identical to an element of constructor form. Eta rules are not part of what may be called canonical Martin-Löf type theory. They are, however, justified by the meaning explanations, and a higher order eta rule is part of that type theory. The main aim of this article is to clarify this somewhat puzzling situation. It will be argued that lower order eta rules do not, whereas the higher order eta rule does, accord with the understanding of judgemental identity as definitional identity. A subsidiary aim is to clarify precisely what an eta rule is. This will involve showing how such rules relate to various other notions of type theory, proof theory, and category theory.

Compiling Hilbert's epsilon operator

Hilbert's epsilon operator is a binder that picks an arbitrary element froma nonempty set. The operator is typically used in logics and proof engines.This paper contributes a discussion of considerations in supporting this operatorin a programming language. More specifically, the paper presents the design choicesmade around supporting this operator in the verification-aware language Dafny.

TIME-VARYING COEFFICIENT MODELS: A PROPOSAL FOR SELECTING THE COEFFICIENT DRIVER SETS

Coefficient drivers are observable variables that feed into time-varying coefficients (TVCs) and explain at least part of their movement. To implement the TVC approach, the drivers are split into two subsets, one of which is correlated with the bias-free coefficient that we want to estimate and the other with the misspecification in the model. This split, however, can appear to be arbitrary. We provide a way of splitting the drivers that takes account of any nonlinearity that may be present in the data, with the aim of removing the arbitrary element in driver selection. We also provide an example of the practical use of our method by applying it to modeling the effect of ratings on sovereign-bond spreads.