A NEW KIND OF THE VARIANT OF THE MODIFIED BERNSTEIN-KANTOROVICH OPERATORS DEFINED BY ¨OZARSLAN AND DUMAN

In the present article, we dene a new kind of the modified Bernstein-Kantorovich operators defined by ¨ Ozarslan (https://doi.org/10.1080/01630563.2015.1079219) i.e. we introduce a new function ς(x) in the modified Bernstein-Kantorovich operators defined by Ozarslan with the property ({) is an infinitely differentiable function on [0; 1]; ς(0) = 0; ς(1) = 1 and ς’(x) > 0 for all x∈ [0; 1]. We substantiate an approximation theorem by using of the Bohman-Korovkins type theorem and scrutinize the rate of convergence with the aid of modulus of continuity, Lipschitz type functions for the our operators and the rate of convergence of functions by means of derivatives of bounded variation are also studied. We study an approximation theorem with the help of Bohman-Korovkins type theorem in A-Statistical convergence. Lastly, by means of a numerical example, we illustrate the convergence of these operators to certain functions through graphs with the help of MATHEMATICA and show that a careful choice of the function ς(x) leads to a better approximation results as compared to the modified Bernstein-Kantorovich operators defined by Ozarslan (https://doi.org/10.1080/01630563.2015.1079219).

A Critical Evaluation of NCERT Mathematics Textbook of Senior Secondary Stage

The aim of the mathematics curriculum at the senior secondary stage is to provide students with an appreciation of the wide variety of the application of mathematics and equip them with the basic tools that enable such application. A careful choice between the often conflicting demands of depth versus breadth needs to be made at this stage. The rapid explosion of mathematics as a discipline, and of its range of application, favors an increase in the breadth of coverage. Such an increase must be dictated by mathematical considerations of the importance of topics to be included. Topics that are more naturally the province of other disciplines may be left out of the mathematics curriculum. The treatment of topics must have an objective, that is, the communication of mathematical insights and concepts, which naturally arouse the interest and curiosity of students.

Are humanized IgE reporter systems potential game changers in serological diagnosis of human parasitic infection?

Immunoglobulin E (IgE) is thought to have evolved to protect mammalian hosts against parasitic infections or toxins and plays a central role in the pathogenesis, diagnosis, and therapy of IgE-mediated allergy. Despite the prominence of IgE responses in most parasitic infections, and in stark contrast to its use in the diagnosis of allergy, this isotype is almost completely unexploited for parasite diagnosis. Here, we discuss the perceived or real limitations of IgE-based diagnosis in parasitology and suggest that the recent creation of a new generation of very sensitive cellular IgE-based reporters may represent a powerful new diagnostic platform, but needs to be based on a very careful choice of diagnostic allergens.

Flexible boundary layer using exchange for embedding theories. I. Theory and implementation

Embedding theory is a powerful computational chemistry approach to exploring the electronic structure and dynamics of complex systems, with QM/MM being the prime example. A challenge arises when trying to apply embedding methodology to systems with diffusible particles, e.g. solvents, if some of them must be included in the QM region, for example in the description of solvent-supported electronic states or reactions involving proton transfer or charge-transfer-to-solvent: without a special treatment, inter-diffusion of QM and MM particles will lead eventually to a loss of QM/MM separation. We have developed a new method called Flexible Boundary Layer using Exchange (FlexiBLE) that solves the problem by adding a biasing potential to the system that closely maintains QM/MM separation. The method rigorously preserves ensemble averages by leveraging their invariance to exchange of identical particles. With a careful choice of the biasing potential, and the use of a tree algorithm to include only important QM and MM exchanges, we find the method has an MM-forcefield-like computational cost and thus adds negligible overhead to a QM/MM simulation. Furthermore, we show that molecular dynamics with the FlexiBLE bias conserves total energy and remarkably, dynamical quantities in the QM region are unaffected by the applied bias. FlexiBLE thus widens the range of chemistry that can be studied with embedding theory.

Efficacy of occlusive wraps used for delivery room care

BackgroundGuidelines advise for more than 20 years to use occlusive plastic wraps for temperature management during delivery room care but data on efficacy of different types of wrap are still scarce.MethodsA random sample of seven different types of plastic wrap was tested using prewarmed aluminium blocks.ResultsThe most effective wrap increased the time to cool by 2°C by one-third for the core and by 100% for the surface whereas the least effective wrap led to even faster heat loss compared with no wrap at all. The least effective wrap concerning all capacities tested was made from polyurethane that contains potentially toxic and narcotic monomers. Heat and water retention did not correlate to wrap thickness.DiscussionLarge differences in heat and water retention capacity warrant a careful choice of the type of wrap as some might be counterproductive. Wraps containing polyurethane should not be used.

Flexible boundary layer using exchange for embedding theories. I. Theory and implementation

Embedding theory is a powerful computational chemistry approach to exploring the electronic structure and dynamics of complex systems, with QM/MM being the prime example. A challenge arises when trying to apply embedding methodology to systems with diffusible particles, e.g. solvents, if some of them must be included in the QM region, for example in the description of solvent-supported electronic states or reactions involving proton transfer or charge-transfer-to-solvent: without a special treatment, inter-diffusion of QM and MM particles will lead eventually to a loss of QM/MM separation. We have developed a new method called Flexible Boundary Layer using Exchange (FlexiBLE) that solves the problem by adding a biasing potential to the system that closely maintains QM/MM separation. The method rigorously preserves ensemble averages by leveraging their invariance to exchange of identical particles. With a careful choice of the biasing potential, and the use of a tree algorithm to include only important QM and MM exchanges, we find the method has an MM-forcefield-like computational cost and thus adds negligible overhead to a QM/MM simulation. Furthermore, we show that molecular dynamics with the FlexiBLE bias conserves total energy and remarkably, dynamical quantities in the QM region are unaffected by the applied bias. FlexiBLE thus widens the range of chemistry that can be studied with embedding theory.

Ionic Liquid-Assisted Grinding: An Electrophilic Fluorination Benchmark

We demonstrated the influence of liquid additives on the rate and selectivity of mechanochemical fluorination of aromatic and 1,3-dicarbonyl compounds with F-TEDA-BF4. Substoichiometric catalytic quantities of ionic liquids speed up the reaction. We proposed an improved protocol for ionic liquids-assisted fluorination that allows easy and efficient isolation of fluorinated products by vacuum sublimation. A careful choice of additive results in high yields of fluorinated products and low E-factor for the overall process. Here, we report a benchmarking study of various ionic liquids in comparison with representative molecular solvents. A lower viscosity of ionic liquid additive is typically associated with higher yields and a higher degree of difluorination. Ionic liquids with fluorous anions (triflate and triflimide) are shown to be the most efficient catalysts for ionic liquid-assisted grinding.

Spanning the isogeny class of a power of an elliptic curve

Let E E be an ordinary elliptic curve over a finite field and g g be a positive integer. Under some technical assumptions, we give an algorithm to span the isomorphism classes of principally polarized abelian varieties in the isogeny class of E g E^g . The varieties are first described as hermitian lattices over (not necessarily maximal) quadratic orders and then geometrically in terms of their algebraic theta null point. We also show how to algebraically compute Siegel modular forms of even weight given as polynomials in the theta constants by a careful choice of an affine lift of the theta null point. We then use these results to give an algebraic computation of Serre’s obstruction for principally polarized abelian threefolds isogenous to E 3 E^3 and of the Igusa modular form in dimension 4 4 . We illustrate our algorithms with examples of curves with many rational points over finite fields.

Quantitative Global-Local Mixing for Accessible Skew Products

We study global-local mixing for a family of accessible skew products with an exponentially mixing base and non-compact fibers, preserving an infinite measure. For a dense set of almost periodic global observables, we prove rapid mixing, and for a dense set of global observables vanishing at infinity, we prove polynomial mixing. More generally, we relate the speed of mixing to the “low frequency behavior” of the spectral measure associated to our global observables. Our strategy relies on a careful choice of the spaces of observables and on the study of a family of twisted transfer operators.

Flexible boundary layer using exchange for embedding theories. I. Theory and implementation

Embedding theory is a powerful computational chemistry approach to exploring the electronic structure and dynamics of complex systems, with QM/MM being the prime example. A challenge arises when trying to apply embedding methodology to systems with diffusible particles, e.g. solvents, if some of them must be included in the QM region, for example in the description of solvent supported electronic states or reactions involving proton transfer or charge-transfer-to-solvent: without a special treatment, inter-diffusion of QM and MM particles will lead eventually to a loss of QM/MM separation. We have developed a new method called Flexible Boundary Layer using Exchange (FlexiBLE) that solves the problem by adding a biasing potential to the system that maintains QM/MM separation. The method rigorously preserves ensemble averages by leveraging their invariance to exchange of identical particles. With a careful choice of the biasing potential, and the use of a tree algorithm to include only important QM and MM exchanges, we find the method has an MM-forcefield-like computational cost and thus adds negligible overhead to a QM/MM simulation. Furthermore, we show that molecular dynamics with the FlexiBLE bias conserves total energy and remarkably, dynamical quantities in the QM region are unaffected by the applied bias. FlexiBLE thus widens the range of chemistry that can be studied with embedding theory.