For Gorenstein quotient spaces C d =G, a direct generalization of the classical McKay correspondence in dimensions d 4 would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces which would satisfy the above property. We prove that the underlying spaces of all Gorenstei...

Let $${\cal M}$$ be an n-cluster tilting subcategory of mod-Λ, where Λ is Artin algebra. S}({\cal M})$$ denote the full S}(\Lambda )$$ , submodule category Λ, consisting all monomorphisms in . We construct two functors from to $$\bmod - \underline {\cal M} $$ finitely presented additive contravariant on stable show that these are full, dense and objective hence provide equivalences between quot...

The sequence (xn)n∈N = (2, 5, 15, 51, 187, . . .) given by the rule xn = (2 n + 1)(2n−1 + 1)/3 appears in several seemingly unrelated areas of mathematics. For example, xn is the density of a language of words of length n with four different letters. It is also the cardinality of the quotient of (Z2 × Z2) under the left action of the special linear group SL(2,Z). In this paper we show how these...

This paper elaborates on the novel intelligence assessment method using the brainwave sub-band power ratio features. The study focuses only on the left hemisphere brainwave in its relaxed state. Distinct intelligence quotient groups have been established earlier from the score of the Raven Progressive Matrices. Sub-band power ratios are calculated from energy spectral density of theta, alpha an...

The only proof of this I know is kind of fiddly and not enlightening. But the point is that in most categories that appear ‘in nature,’ regular, strong, and extremal epics are about the same, and all are the correct notion of quotient, while ordinary epimorphisms may not be. For example, N→ Q is epic in Rings, but not extremal epic. In Top the epics are the surjective maps, while the regular = ...

Adversity quotient is the capacity to adjust with the adversities in life. A person with good Adversity quotient can achieve the goal by fighting against all odds. It is also related to many other factors like self esteem, motivation, fighting spirit, creativity, sincerity, positive attitude, optimism, emotional stability etc. Adversity quotient is also related to the Academic problems of stude...

The convex PBW-type Lyndon basis for two-parameter quantum group Ur,s (F4)is given. Assume that rs−1 is a primitive ℓ-th root of unity with ℓ odd, then the restricted $${\mathfrak{u}_{r,s}}({F_4})$$ as quotient Ur,s(F4) pointed, and Drinfel’d double structure under certain condition. All Hopf isomorphisms are determined, necessary sufficient condition to be ribbon algebra singled out by describ...