Phase and structural order in mixture of nematic liquid crystals and anisotropic nanoparticles

We studied the structural order in randomly perturbed nematic liquid crystals using a random anisotropic nematic-type lattice model. Simulations were carried out at zero temperature and at various other temperatures, for which we varied the concentration of impurities p, anchoring strength W and imposed external strength fields B at two different histories: temperature-quenched history (TQH) and field-quenched history. The Haller approximation method utilized the temperature dependence of the order parameter to determine the pseudo-critical exponent β at different values of p and W. Consequently, the values of β increased when p and W were increased. Additionally, applying an external field B for investigating the parameters revealed that the TQH established long-range order for high magnitudes of B at zero temperature (T* = 0) and T* = 0.5.     

Synthesis and Evaluation of Antioxidant Properties of 2-Substituted Quinazolin-4(3H)-ones

Quinazolinones represent an important scaffold in medicinal chemistry with diverse biological activities. Here, two series of 2-substituted quinazolin-4(3H)-ones were synthesized and evaluated for their antioxidant properties using three different methods, namely DPPH, ABTS and TEAC_CUPRAC, to obtain key information about the structure–antioxidant activity relationships of a diverse set of substituents at position 2 of the main quinazolinone scaffold. Regarding the antioxidant activity, ABTS and TEAC_CUPRAC assays were more sensitive and gave more reliable results than the DPPH assay. To obtain antioxidant activity of 2-phenylquinazolin-4(3H)-one, the presence of at least one hydroxyl group in addition to the methoxy substituent or the second hydroxyl on the phenyl ring in the ortho or para positions is required. An additional ethylene linker between quinazolinone ring and phenolic substituent, present in the second series (compounds 25a and 25b), leads to increased antioxidant activity. Furthermore, in addition to antioxidant activity, the derivatives with two hydroxyl groups in the ortho position on the phenyl ring exhibited metal-chelating properties. Our study represents a successful use of three different antioxidant activity evaluation methods to define 2-(2,3-dihydroxyphenyl)quinazolin-4(3H)-one 21e as a potent antioxidant with promising metal-chelating properties.     

Combined swept region and intersection‐based single‐material remapping method

A typical arbitrary Lagrangian–Eulerian algorithm consists of a Lagrangian step, where the computational mesh moves with the fluid flow; a rezoning step, where the computational mesh is smoothed and repaired in case it gets too distorted; and a remapping step, where all fluid quantities are conservatively interpolated on this new mesh. In single‐material simulations, the remapping process can be represented in a flux form, with fluxes approximated by integrating a reconstructed function over intersections of neighboring computational cells on the original and rezoned computational mesh. This algorithm is complex and computationally demanding – Therefore, a simpler approach that utilizes regions swept by the cell edges during rezoning is often used in practice. However, it has been observed that such simplification can lead to distortion of the solution symmetry, especially when the mesh movement is not bound by such symmetry. For this reason, we propose an algorithm combining both approaches in a similar way that was proposed for multi‐material remapping (two‐step hybrid remap). Intersections and exact integration are employed only in certain parts of the computational mesh, marked by a switching function – Various different criteria are presented in this paper. The swept‐based method is used elsewhere in areas that are not marked. This way, our algorithm can retain the beneficial symmetry‐preserving capabilities of intersection‐based remapping while keeping the overall computational cost moderate.     

On the resolution of time problem in quantum gravity induced from unconstrained membranes

The relativistic theory of unconstrained p-dimensional membranes (p-branes) is further developed and then applied to the embedding model of induced gravity. Space-time is considered as a 4-dimensional unconstrained membrane evolving in an N-dimensional embedding space. The parameter of evolution or the evolution time is a distinct concept from the coordinate time t=x⁰. Quantization of the theory is also discussed. A covariant functional Schrödinger equation has a solution for the wave functional such that it is sharply localized in a certain subspace P of space-time, and much less sharply localized (though still localized) outside P. With the passage of evolution the region P moves forward in space-time. Such a solution we interpret as incorporating two seemingly contradictory observations: (i) experiments clearly indicate that space-time is a continuum in which events are existing; (ii) not the whole 4-dimensional space-time, but only a 3-dimensional section which moves forward in time, is accessible to our immediate experience. The notorious problem of time is thus resolved in our approach to quantum gravity. Finally we include sources into our unconstrained embedding model.     

On a certain identity satisfied by a derivation and an arbitrary additive mapping II

Summary The structure of prime ringsR and nonzero derivationsd onR, satisfyingd(x)f(x) = 0 for allx R, is described,f being a nonzero additive mapping ofR. Supported in part by a grant from the Ministry of Science of Slovenia.     

Mechanochemistry as a versatile and scalable tool for nanomaterials synthesis: Recent achievements in Košice,Slovakia

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Synthese der Clathratverbindungen des Typs Cd(en)Pd(CN)4·2G

In this paper three compounds with the same host molecule of Cd(en)Pd(CN)₄ type, but of different organic components such as thiophene, pyrrole and furan were described.     

Functional Identities and Rings of Quotients

The fundamental theorem on functional identities states that a prime ring R with \(\deg (R)\ge d\) is a d-free subset of its maximal left ring of quotients Q _{m l} (R). We consider the question whether the same conclusion holds for symmetric rings of quotients. This indeed turns out to be the case for the maximal symmetric ring of quotients Q _{m s} (R), but not for the symmetric Martindale ring of quotients Q _s (R). We show, however, that if the maps from the basic functional identities have their ranges in R, then the maps from their standard solutions have their ranges in Q _s (R). We actually prove a more general theorem which implies both aforementioned results. Its proof is somewhat shorter and more compact than the standard proof used for establishing d-freeness in various situations.