Mod-2 dihedral Galois representations of prime conductor

For all odd primes N up to 500000, we compute the action of the Hecke operator T_2 on the space S_2(Gamma_0(N), Q) and determine whether or not the reduction mod 2 (with respect to a suitable basis) has 0 and/or 1 as eigenvalues. We then partially explain the results in terms of class field theory and modular mod-2 Galois representations. As a byproduct, we obtain some nonexistence results on elliptic curves and modular forms with certain mod-2 reductions, extending prior results of Setzer, Hadano, and Kida

Phosphorous compounds in leather industry

The possible applications of phosphorus compounds in leather-making are reviewed. Polyphosphoric acid or its salts are used as (a) pretanning agent in vegetable tanning and (b) pretanning or retaining agent or complexing component in chrome lanning, Polyphosphates are also water softeners, The phospho-compound tetrakis (hydroxy methyl) phosphonium chloride is a good tanning agent in the presence of resorcinol. Phosphatides and alkyl phospho-esters are complexing lubricants. Chrome complexes of alkyl phosphoesters are water proofing-agents. Phospho-acrylates are good additives to acrylic finishes for impairing flame-proof characterstics. Poly-fluoro alkyl phosphates impart oil repellent characterstics in leathers. Triaryl phosphates are good plasticisers for vinyl and cellulosie finishes; they are also flame-retardents

Science and technology of chrome tanning

This article does not have an abstract

Thermoset leather finish

This article does not have an abstract

Oleophobic and hydro phobic properties of fluoro compounds and their application in leather making

Application of fluoro compounds in leather making is surveyed. The theory behind the oil and water repelling mechanisms of fluoral chemicals is explained. The importance of various types of fluoro chemicals, such as fluoro acrylics, copolymers of fluorine containing monomers, fluoro silicones, phosphorous containing fluoro acrylics is highlighted. Fungicide and disinfectant properties of fluoro compounds on leather are reported. Possible developments and application of these fluoro chemicals in leather making are suggested

An interesting case of neurocutaneous syndrome

Neuroichthyosis is a group of rare genetically determined disease with cutaneous and neurological manifestations due to abnormalities in any of the following: lipid metabolism, glycoprotein synthesis, or intracellular vesicle trafficking. There are about 16 disorders with known genetic aetiology like Sjogren Larssons syndrome (SLS), Refsum disease, Gauchers disease type 2, ELOVL4 deficiency etc. Among the various neuroicthyosis syndromes, Sjogren Larsson syndrome is the most common entity characterised by ichthyosis, spastic diplegia or tetraplegia, cognitive dysfunction, seizures, and a maculopathy with glistening white dots. We hereby report a case of neuroichthyosis disease who presented to us with developmental delay, spastic paraplegia, seizure and ichthyosis, whose genetic testing showed homozygous mutation in ALDH3A2, suggestive of Sjogren Larsson syndrome

Easy care finishes based urethane leather. Part I

This article does not have an abstract

Testing Hardy nonlocality proof with genuine energy-time entanglement

We show two experimental realizations of Hardy ladder test of quantum nonlocality using energy-time correlated photons, following the scheme proposed by A. Cabello \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 040401 (2009)]. Unlike, previous energy-time Bell experiments, these tests require precise tailored nonmaximally entangled states. One of them is equivalent to the two-setting two-outcome Bell test requiring a minimum detection efficiency. The reported experiments are still affected by the locality and detection loopholes, but are free of the post-selection loophole of previous energy-time and time-bin Bell tests.Comment: 5 pages, revtex4, 6 figure

An interesting case of anhidrosis

Ross syndrome is a rare syndrome of autonomic dysfunction which is characterized by segmental hypohidrosis/ anhidrosis, Adie tonic pupil and hyporeflexia/areflexia. Exact etiology is not known. It was first described in 1958 and approximately 50 cases have been described so far globally. We hereby report a case of segmental anhidrosis of left face, left upper limb and left side of chest with 3-year duration in a 26-year-old man who also had Adie’s tonic pupil in right eye and global areflexia on examination

A quotient of the Lubin-Tate tower II

In this article we construct the quotient M_1/P(K) of the infinite-level Lubin-Tate space M_1 by the parabolic subgroup P(K) of GL(n,K) of block form (n-1,1) as a perfectoid space, generalizing results of one of the authors (JL) to arbitrary n and K/Q_p finite. For this we prove some perfectoidness results for certain Harris-Taylor Shimura varieties at infinite level. As an application of the quotient construction we show a vanishing theorem for Scholze's candidate for the mod p Jacquet-Langlands and the mod p local Langlands correspondence. An appendix by David Hansen gives a local proof of perfectoidness of M_1/P(K) when n = 2, and shows that M_1/Q(K) is not perfectoid for maximal parabolics Q not conjugate to P.Comment: with an appendix by David Hanse