The articles [16], [9], [19], [18], [13], [1], [6], [21], [5], [10], [12], [17], [20], [7], [8], [15], [11], [2], [3], and [4] provide the notation and terminology for this paper. We consider structures of the type algebra as extensions of 1-sorted structure as systems 〈 a carrier, a left quotient, a right quotient, an inner product 〉, where the carrier is a set and the left quotient, the right...

We prove that a space is quotient π-image of a locally separable metric space if and only if it has a πand double cs∗cover. We also investigate quotient π-s-images of locally separable metric spaces.

This research aims to categorize the mathematics anxiety and adversity quotient in students describe profile of based on quotient. method is qualitative with a case study design. The subjects this were 45 SMPIT Sabilul Huda. data collection instruments used Taylor Manifest Anxiety Scale (TMAS), Adversity Quotient Response Profile (ARP) scale, interview guidelines. Data analysis techniques are r...

In algebraic geometry one often encounters the problem of taking the quotient of a scheme by a group. Despite the frequent occurrence of such problems, there are few general results about the existence of such quotients. These questions come up again and again in the theory of moduli spaces. When we want to classify some type of algebraic objects, say varieties or vector bundles, the classifica...

It is shown that certain weak-base structures on a topological space give a D-space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are D-spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Theorem. Any symmetrizable space X is a D-space (hereditarily). Hence, quotient mappings, with compact fibers, from metric s...

Z. Li characterized spaces with a weak-development consisting of point-countable sfp-covers by pseudo-sequence-covering, quotient, and π-s-image of metric spaces. In this paper, we omit ”pseudo-sequence-covering” in the above result, and prove that a space has a weak-development consisting of point-countable sfp-covers iff it is a quotient, and π-s-image of a metric space.

The problem of constructing moduli space of vector bundles over a projective manifold has attracted many mathematicians for decades. In mid 60’s Mumford first constructed the moduli space of vector bundles over algebraic curves via his celebrated GIT machinery. Later, in early 80’s Atiyah and Bott found an infinite dimensional symplectic quotient description of this moduli space. Since then, we...

The quotient correlation is defined here as an alternative to Pearson’s correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation coefficient is generally not applicable. One of its most useful features is a test statistic that has high power when testing nonlinear dependence in cases whe...

the concept of right (left) quotient (or residual) of an ideal η by anideal ν of an l-subring μ of a ring r is introduced. the right (left) quotients areshown to be ideals of μ . it is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an l-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . most of the results pertaining to the notion of quotients(or residual) of ...

For a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of g over S. Given a maximal torus T with Lie algebra t and associated Weyl group W , we show that the Chevalley morphism π : t/W → g/G is an isomorphism except for the group Sp2n over a base with 2-torsion...