Recently, Marian–Oprea–Pandharipande established (a generalization of) Lehn's conjecture for Segre numbers associated to Hilbert schemes of points on surfaces. Extending the work Johnson, they provided a conjectural correspondence between and Verlinde numbers. For surfaces with holomorphic 2-form, we propose generalizations their results moduli spaces stable sheaves any rank. Using Mochizuki's ...

Let T x be the full transformation semigroup on the set X and let S be a subsemigroup of Tx. We may associate with S a digraph g(5) with X as set of vertices as follows: / —► / e g(<S) iff there exists a 6 S such that a(i) = /. Conversely, for a digraph C having certain properties we may assign a semigroup structure, S(G), to the underlying set of G. We are thus able to establish a "Galois corr...

The main objective of this paper is to show that the notion of type which was developed within the frames of logic and model theory has deep ties with geometric properties of algebras. These ties go back and forth from universal algebraic geometry to the model theory through the machinery of algebraic logic. We show that types appear naturally as logical kernels in the Galois correspondence bet...

We present 15 new partial difference sets over 4 non-abelian groups of order 100 and 2 new strongly regular graphs with intransitive automorphism groups. The strongly regular graphs and corresponding partial difference sets have the following parameters: (100,22,0,6), (100,36,14,12), (100,45,20,20), (100,44,18,20). The existence of strongly regular graphs with the latter set of parameters was a...

From an arbitrary temporal logic institution we show how to set-up the corresponding institution of objects. The main properties of the resulting institution are studied and used in establishing the denotational, categorial semantics of several basic object specification constructs, namely aggregation (parallel composition), interconnection, abstraction (interfacing) and monotonic specializatio...

Scholze and Shin [J. Amer. Math. Soc. 26 (2013), pp. 261–294] gave a conjectural formula relating the traces on automorphic Galois sides of local Langlands correspondence. Their work generalized an earlier Scholze, which he used to give new proof conjecture for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper G normal L S...

The local Langlands correspondence is a conjectural connection between representations of groups G(k) for connected reductive groups G over a p-adic field k and certain homomorphisms (Langlands parameters) from the Galois (or WeilDeligne group) of k into a complex Lie group Gwhich is dual, in a certain sense, to G and which encodes the splitting structure of G over k. More introductory remarks ...

A completely primary finite ring is a ring R with identity 1 = 0 whose subset of all its zero divisors forms the unique maximal ideal J . Let R be a commutative completely primary finite ring with the unique maximal ideal J such that J3 = (0) and J2 = (0). Then R/J ∼= GF(pr) and the characteristic of R is pk, where 1≤ k ≤ 3, for some prime p and positive integer r. Let Ro =GR(pkr , pk) be a Gal...

It is shown that the convenient processing facilities of digital signals varying in a finite range amplitudes are non-binary Galois fields, numbers which elements equal to prime numbers. Within choosing sampling interval corresponding such field, it becomes possible construct field Fourier transform, distinctive feature exact correspondence with ranges variation original signal and its spectrum...

Évariste Galois (1811–1832) has been increasingly recognised as an important mathematician who despite his short life developed mathematical ideas that today have led to applications in computer science (such as Galois connections) and elsewhere. Some of Galois’ mathematics can be visualised in interesting and even artistic ways, aided using software. In addition, a significant corpus of the hi...