In the title compound, C22H15Cl2FO2, a chalcone derivative featuring a threefold-halogenated aromatic substituent, the conformation about the C=C bond is E. In the crystal C-H⋯F and C-H⋯Cl contacts connect the mol-ecules into undulating sheets parallel to (101). In addition, C-H⋯π inter-actions are also present.

THE TITLE COMPOUND (SYSTEMATIC NAME rac-3,3,3-trifluoro-2-hy-droxy-propanoic acid), C3H3F3O3, is a fluorinated derivative of lactic acid. The O=C-C-O(H) torsion angle is 13.26 (15)°. In the crystal, O-H⋯O hydrogen bonds and C-H⋯O contacts connect the mol-ecules into sheets perpendicular to the c axis.

In the crystal structure of the title amino alcohol derivative, C(9)H(24)N(2)O(2+)·2Cl(-), the cations and anions are linked by inter-molecular O-H⋯Cl and N-H⋯Cl hydrogen bonds into a three-dimensional network.

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra H∞[b : b has finite angular derivative everywhere]. We study the most well-known example of a Blaschke product with infinite angular deriva...

We survey recent results on the structure of the range of the derivative of a smooth mapping f between two Banach spaces X and Y . We recall some necessary conditions and some sufficient conditions on a subsetA of (X ,Y) for the existence of a Fréchet differentiable mapping f from X into Y so that f ′(X)= A. Whenever f is only assumed Gâteaux differentiable, new phenomena appear: for instance, ...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

potential field methods such as gravity and magnetic methods are among the most applied geophysical methods in mineral exploration. a high-resolution technique is developed to image geologic boundaries such as contacts and faults. potential field derivatives are the basis of many interpretation techniques. in boundary detection, the analytic signal quantity is defined by combining the val...

The dynamical evolution of the Hajicek 1-form is derived in Einstein-Cartan (EC) theory. We find that like Einstein theory gravity, equation related to a projected part tensor (${\stackrel{^}{G}}_{ab}$) on generic null surface $\mathcal{H}$, particularly ${\stackrel{^}{G}}_{ab}{l}^{a}{{q}^{b}}_{c}$, where ${l}^{a}$ and ${{q}^{a}}_{c}$ are outgoing generators $\mathcal{H}$ induced metric transve...

In this paper, authors study the concept of (s,m)-exponential type convex functions and their algebraic properties. New generalizations Hermite-Hadamard inequality for function ? products two are proved. Some refinements (H-H) whose first derivative in absolute value at certain power obtain. Finally, many new bounds special means error estimates trapezoidal midpoint formula provided as well.

A quantum mechanical system describing bosons in one space dimension with a kinetic energy of arbitrary order in derivatives and a delta function interaction is studied. Exact wavefunctions for an arbitrary number of particles and order of derivative are constructed. Also, equations determining the spectrum of eigenvalues are found. PACS numbers: 02.30Jr, 05.30Jp Physical systems whose equation...