In the title compound, C(12)H(15)N(3)O(2), the dihedral angle between the mean planes of the benzene and triazole rings is 0.331 (53) °. The side chain of the pivalate unit forms a dihedral angle of 69.04 (12)° with the benzotriazole unit. The ester group and two methyl groups of the pivalate unit are disordered with an occupancy ratio of 0.731 (3):0.269 (3). In the crystal, weak π-π stacking i...

The asymmetric unit of the title compound, C(18)H(21)N(3)S, contains five mol-ecules. The equivalent bond distances in the five mol-ecules are in excellent agreement, the r.m.s. fit being within 0.007 Å. The five mol-ecules are linked into a chain consisting of alternating pseudo-enanti-omers by N-H⋯S hydrogen bonds supplemented by weak C-H⋯π inter-actions. The action of a glide plane links the...

In this paper we revisit Wiener’s method (IEEE-IT 1990) of continued fraction (CF) to find new weaknesses in RSA. We consider RSA with N = pq, q < p < 2q, public encryption exponent e and private decryption exponent d. Our motivation is to find out when RSA is insecure given d is O(N), where we are mostly interested in the range 0.3 ≤ δ ≤ 0.5. Given ρ (1 ≤ ρ ≤ 2) is known to the attacker, we sh...

This complements the work of [2] on the construction of scales of minimal complexity on sets of reals in K(R). Theorem 0.1 was proved there under the stronger hypothesis that all sets definable over M are determined, although without the capturing hypothesis. (See [2, Theorem 4.14].) Unfortunately, this is more determinacy than would be available as an induction hypothesis in a core model induc...

Starting from a logic which speciies how to make deductions from a set of sentences (a ``at theory'), a way to generalise this to a partially ordered bag of sentences (a `structured theory') is given. The partial order is used to resolve connicts. If occurs below then is accepted only insofar as it does not connict with. We start with a language L, a set of interpretations M and a satisfaction ...

in this paper, three dimensional (3d) static and dynamic analysis of thick plates based on the meshless local petrov-galerkin (mlpg) is presented. using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. a weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...

novel electron-rich fused aromatic unit, namely benzo[1,2-b:3,4b’:5,6-d’’]trithiophene (BTT), which holds promise as a building block for semiconductor materials. In comparison with the wellknown benzo[1,2-b:4,5-b’]dithiophene (BDT), quantumchemical calculations (B3LYP/6-31G*) predict the BTT unit to 40 be of similar donor strength. Thus, with R being alkyl chains, BTT is predicted to act as a ...

In the title chalcone derivative, C(13)H(8)Cl(2)OS, the prop-2-en-1-one unit and the thio-phene and 2,4-dichloro-phenyl rings are each essentially planar. The inter-planar angle between the thio-phene and 2,4-dichloro-phenyl rings is 19.87 (6)°. Weak intra-molecular C-H⋯O and C-H⋯Cl inter-actions involving the prop-2-en-1-one unit generate an S(5)S(5) ring motif. In the crystal structure, mol-e...

In the mol-ecules of the title compounds, (2E)-1-(3-bromo-thio-phen-2-yl)-3-(2-meth-oxy-phen-yl)prop-2-en-1-one, C14H11BrO2S, (I), which crystallizes in the space group P-1 with four independent mol-ecules in the asymmetric unit (Z' = 8), and (2E)-1-(3-bromo-thio-phen-2-yl)-3-(3,4-di-meth-oxy-phen-yl)prop-2-en-1-one, C15H13BrO3S, (II), which crystallizes with Z' = 8 in the space group I2/a, the...

We show that every braided monoidal category arises as End(I) for a weak unit I in an otherwise completely strict monoidal 2-category. This implies a version of Simpson’s weak-unit conjecture in dimension 3, namely that one-object 3-groupoids that are strict in all respects, except that the object has only weak identity arrows, can model all connected, simply connected homotopy 3-types. The pro...