Let $X$ be a smooth projective variety. We show that the map sends codimension one distribution on to its singular scheme is morphism from moduli space of distributions into Hilbert scheme. describe fibers and, when $X = \mathbb{P}^n$, compute them via syzygies. As an application, we spaces degree 1 $\mathbb{P}^3$. also give minimal graded free resolution for ideal generic

The use of algorithms in algebra as well as the study of their complexity was initiated before the advent of modern computers. Hermann [25] studied the ideal membership problem, i.e determining whether a given polynomial is in a fixed homogeneous ideal, and found a doubly exponential bound on its computational complexity. Later Mayr and Meyer [31] found examples which show that her bound was ne...

We report that high-density single-molecule super-resolution microscopy can be achieved with a conventional epifluorescence microscope set-up and mercury arc lamp. The configuration termed as laser-free (LFSM) is an extension of localization (SMLM) techniques allows single molecules to switched on off (a phenomenon ‘blinking’), detected localized. use short burst deep blue excitation (350–380 n...

second order advantage of excitation-emission fluorescence matrix was applied for the simultaneous determination of ibuprofen and caffeine. the proposed method is based on the measurement of the native fluorescence and recording emission spectra of ibuprofen and caffeine in different excitation wavelengths. the mixture of these compounds was resolved by multivariate curve resolution coupled wit...

Suppose that G is a linearly reductive group. Good degree bounds for generators of invariant rings were given in [2]. Here we study the minimal free resolution of the invariant ring. Recently it was shown that if G is a finite linearly reductive group, then the ring of invariants is generated in degree ≤ |G| (see [5, 6, 3]). This extends the classical result of Noether who proved the bound in c...

Six test dental radiographic films with varying resolutions and exposure times were evaluated diagnostically by 334 dentists. Each dentist completed a questionnaire relative to observations, dental education, practice profile, film utilization, and opinions on how electronic enhancement of the film affected his diagnostic ability. More than 60% identified 12-20 paired lines per mm of resolution...

We describe a presentation of glycogenic hepatopathy in a poorly controlled type I diabetic patient. As patients with glycogenic hepatopathy often have nonspecific complaints, diagnosis tends to be delayed and laboratory and imaging data are often indistinguishable from nonalcoholic fatty liver disease. Our patient's diagnosis of glycogenic hepatopathy required a liver biopsy, which demonstrate...

If r ≥ 6, r 6= 9, we show that the Minimal Resolution Conjecture fails for a general set of γ points in P for almost 12 √ r values of γ. This strengthens the result of Eisenbud and Popescu [1999], who found a unique such γ for each r in the given range. Our proof begins like a variation of that of Eisenbud and Popescu, but uses exterior algebra methods as explained by Eisenbud and Schreyer [200...

Two ideals I and J are called transverse if ∩ = . We show that the obstructions defined by Avramov for products of (sequentially) in regular local rings always 0. In particular, we compute an explicit free resolution Koszul homology all such ideals. Moreover, construct trivial Massey operation on associated complex hence (by Golod's construction) a minimal residue field over quotient product co...