Progressive Compression of 3D Mesh Geometry Using Sparse Approximations from Redundant Frame Dictionaries

In this paper, we present a new approach for the progressive compression of three‐dimensional (3D) mesh geometry using redundant frame dictionaries and sparse approximation techniques. We construct the proposed frames from redundant linear combinations of the eigenvectors of a combinatorial mesh Laplacian matrix. We achieve a sparse synthesis of the mesh geometry by selecting atoms from a frame using matching pursuit. Experimental results show that the resulting rate‐distortion performance compares favorably with other progressive mesh compression algorithms in the same category, even when a very simple, sub‐optimal encoding strategy is used for the transmitted data. The proposed frames also have the desirable property of being able to be applied directly to a manifold mesh having arbitrary topology and connectivity types; thus, no initial remeshing is required and the original mesh connectivity is preserved.     

Anti-inflammatory activity of heterocyclic systems using abietic acid as starting material

A series of pyridines, pyrimidinone, oxazinones, and their derivatives were synthesized as anti-inflammatory agents using abietic acid (7-isopropyl-1,4a-dimethyl-1,2,3,4,4a,4b,5,6,10,10a-decahydrophenanthrene-1-carboxylic acid) as the starting material. The arylidiene derivative was treated with cyanothioacetamide to give cyano pyridine-thione, which was reacted with ethyl chloroacetate to yield the corresponding cyano ester. The ester was hydrolysed to the sodium salt, which was reacted with acetic anhydride to afford 2-methyloxazinone, which was treated with ammonium acetate to afford 2-methylpyrimidinone followed by methylation with methyl iodide to yield 2,3-dimethyl- pyrimidinone. In addition, the oxazinone derivative was reacted with aniline or hydrazine hydrate to give 3-phenyl- or 3-aminopyrimidinones. The latter reacted with thiophene-2-carboxaldehyde or phenylisothiocyanate to afford Schiff’s bases or thiosemicarbazide derivatives. The pharmacological screening showed that many of these compounds have good anti-inflammatory activity comparable to Prednisolone^® as reference drug.     

Simultaneous Quantification of Seven Flavonoids in Flos Gossypii by LC

Species of the genus Achillea have been used in traditional folk medicine for centuries. In Europe taxa of the Achillea millefolium group are widely spread, their correct taxonomic differentiation by morphological and anatomical characteristics encounters some difficulties. Several species of the polyploid A. millefolium group however, can be characterised by their distinct sesquiterpene pattern. Analysis is usually performed by LC using conventional RP stationary phases. Likewise, it has been proven that non-porous RP stationary phases are an excellent alternative for sensitive and more rapid separations of plant extracts. In the present work a Kovasil MS-C18 1.5 μm non-porous packing was used with an acetonitrile-water gradient for the analysis of Achillea flower extracts. Detection and identification of the respective sesquiterpenes has been achieved by diode array detection and LC coupled APCI+ and ESI+ mass spectrometry.     

Liouville Theorems for a General Class of Nonlocal Operators

In this paper, we study the equation \(\mathcal {L} u=0\) in \(\mathbb {R}^{N}\), where \(\mathcal {L}\) belongs to a general class of nonlocal linear operators which may be anisotropic and nonsymmetric. We classify distributional solutions of this equation, thereby extending and generalizing recent Liouville type theorems in the case where \(\mathcal {L}= (-{\Delta })^{s}\), s ∈ (0, 1) is the classical fractional Laplacian.     

Multi-armed bandits based on a variant of Simulated Annealing

A variant of Simulated Annealing termed Simulated Annealing with Multiplicative Weights (SAMW) has been proposed in the literature. However, convergence was dependent on a parameter β(T), which was calculated a-priori based on the total iterations T the algorithm would run for. We first show the convergence of SAMW even when a diminishing stepsize β_k → 1 is used, where k is the index of iteration. Using this SAMW as a kernel, a stochastic multi-armed bandit (SMAB) algorithm called SOFTMIX can be improved to obtain the minimum-possible log regret, as compared to log² regret of the original. Another modification of SOFTMIX is proposed which avoids the need for a parameter that is dependent on the reward distribution of the arms. Further, a variant of SOFTMIX that uses a comparison term drawn from another popular SMAB algorithm called UCB1 is then described. It is also shown why the proposed scheme is computationally more efficient over UCB1, and an alternative to this algorithm with simpler stepsizes is also proposed. Numerical simulations for all the proposed algorithms are then presented.     

Determination of total chromium in phosphate rocks by ion chromatography

Chromium(VI) is one of seven elements which is classified in the fertilizer industry as being harmful to plants and biological systems. Phosphate rocks represent the raw material for complex fertilizer production in the world. This paper investigates for the first time the determination of total chromium in phosphate rocks by ion chromatography. The developed analytical method involves the digestion of phosphate rocks with nitric acid followed by sample treatment of the resulting solution. The digestion solution obtained was treated with an oxidising agent (potassium peroxosulphate) to convert all chromium to the hexavalent state. The analytical method developed utilizes anion-exchange ion chromatography to achieve the separation and spectrophotometric post-column reaction for detection with diphenylcarbazide. The relative standard of deviation from analytical data comparison of six different phosphate rocks with atomic absorption spectrometry and inductively coupled plasma atomic emission spectrometry techniques, and cross-analysis data against an internationally certified phosphate rock standard were between 0.58 and 1.45%. Calibration curve between 0.2 and 0.9 μg/ml was excellent, and the method has a detection limit for Cr(VI) of 0.05 ng. The developed method offers a fast, a reliable and an alternative procedure for the determination of total chromium in phosphate rock deposits by ion chromatography.     

A green synthetic approach toward the synthesis of structurally diverse spirooxindole derivative libraries under catalyst-free conditions

A catalyst-free green methodology for the synthesis of pharmacologically important spirooxindole derivatives has been developed by a three-component domino reaction between isatin, various amino compounds, and 1,3-dicarbonyl or 3-phenylisoxazolone compounds in ethyl l-lactate medium at room temperature. This new efficient synthetic method facilitated the formation of a wide range of biologically significant spirooxindole derivatives (including 17 new spirooxindoles) under very mild conditions. The cytotoxic activity of one of the isoxazole-fused spirooxindoles was evaluated in MDA-MB 468 breast cancer cell line. It was found that cell survivability decreases with increasing concentration of the selected compound in MDA-MB 468 breast cancer cells.     

Observational constraints on the jerk parameter with the data of the Hubble parameter

We study the accelerated expansion phase of the universe by using the kinematic approach. In particular, the deceleration parameter q is parametrized in a model-independent way. Considering a generalized parametrization for q, we first obtain the jerk parameter j (a dimensionless third time derivative of the scale factor) and then confront it with cosmic observations. We use the latest observational dataset of the Hubble parameter H(z) consisting of 41 data points in the redshift range of \(0.07 \le z \le 2.36\), larger than the redshift range that covered by the Type Ia supernova. We also acquire the current values of the deceleration parameter \(q_0\), jerk parameter \(j_0\) and transition redshift \(z_t\) (at which the expansion of the universe switches from being decelerated to accelerated) with \(1\sigma \) errors (\(68.3\%\) confidence level). As a result, it is demonstrate that the universe is indeed undergoing an accelerated expansion phase following the decelerated one. This is consistent with the present observations. Moreover, we find the departure for the present model from the standard \(\Lambda \)CDM model according to the evolution of j. Furthermore, the evolution of the normalized Hubble parameter is shown for the present model and it is compared with the dataset of H(z).