Semidefinite Approximations of the Matrix Logarithm

Foundations of Computational Mathematics - The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator...     

The sum-of-squares hierarchy on the sphere and applications in quantum information theory

Mathematical Programming - We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of sum-of-squares relaxations. Exploiting the polynomial kernel...     

Geological and radioactivity studies accompanied by uranium recovery: Um Bogma Formation,southwestern Sinai,Egypt

Journal of Radioanalytical and Nuclear Chemistry - High radioactive anomalies were recorded in the variegated claystones at the middle member of Um Bogma Formation, the eU-content reaches...     

Effect of Nano‐support and Type of Active Metal on Reforming of CH4 with CO2

Two series of Co and Ni based catalysts supported over commercial (ZrO₂, CeO₂, and Al₂O₃) nano supports were investigated for dry reforming of methane. The catalytic activity of both Co and Ni based catalysts were assessed at different reaction temperatures ranging from 500—800 °C; however, for stability the time on stream experiments were conducted at 700 °C for 6 h. Various techniques such as N₂ adsorption‐desorption isotherm, temperature‐programmed reduction (H₂‐TPR), temperature‐programmed desorption (CO₂‐TPD), temperature‐programmed oxidation (TPO), X‐ray diffraction (XRD), thermogravimetric analysis (TGA) were applied for characterization of fresh and spent catalysts. The catalytic activity and stability tests clearly showed that the performance of catalyst is strongly dependent on type of active metal and support. Furthermore, active metal particle size and Lewis basicity are key factors which have significant influence on catalytic performance. The results indicated that Ni supported over nano ZrO₂ exhibited highest activity among all tested catalysts due to its unique properties including thermal stability and reducibility. The minimum carbon deposition and thus relatively stable performance was observed in case of Co‐Al catalyst, since this catalyst has shown highest Lewis basicity.     

Reactions with cyclic amidines II. The behaviour of cyclic amidines toward ethoxycarbonyl and aroyl isothiocyanates

The behaviour of the aminopyrazole derivatives 1a-c, 2-amino-4-phenylthiazole (2) and 2-amino-5-phenyl-1,3,4-thiadiazole (3) toward the action of ethoxycarbonyl and benzoyl iso-thiocyanate is reported. The data clearly demonstrates the dependence of the nature of the products obtained from the reaction of isothiocyanates with cyclic amidines on the nature of the substituents on the heterocyclic ring.     

Localization for Random Unitary Operators

We consider unitary analogs of one-dimensional Anderson models on defined by the product U _ω=D _ω S where S is a deterministic unitary and D _ω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of U _ω is pure point almost surely for all values of the parameter of S. We provide similar results for unitary operators defined on together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunsky coefficients of constant modulus and correlated random phases Mathematics Subject Classification. 82B44, 42C05, 81Q05     

Operational rules and a generalized Hermite polynomials

In this paper, we use operational rules associated with three operators corresponding to a generalized Hermite polynomials introduced by Szegö to derive, as far as we know, new proofs of some known properties as well as new expansions formulae related to these polynomials.     

Investigations on the structure of 4-methyldihydro-1,3,4-benzotriazepin-5-ones. Tautomer reassignment

The tautomerism of 4-methyldihydro-1,3,4-benzotriazepin-5-ones (2,3) is re-investigated by means of X-ray diffraction and quantum chemical calculations. The data revealed that the model compound (2a) exists in the amidrazone 1,4-dihydro tautomeric form (A), but not in the alternate 3,4-dihydro tautomer (B) as was previously reported.     

Thymus algeriensis and Artemisia herba-alba Essential Oils: Chemical Analysis,Antioxidant Potential and In Vivo Anti-Inflammatory,Analgesic Activities,and Acute Toxicity

The study of bioactive molecules of natural origin is a focus of current research. Thymus algeriensis and Artemisia herba-alba are two medicinal plants widely used by the Moroccan population in the traditional treatment of several pathologies linked to inflammation. This study aimed to evaluate the single and combined antioxidant, anti-inflammatory and analgesic effects of the essential oils extracted from these two medicinal plants, and also their potential toxicity. Essential oils were extracted using hydro-distillation in a Clevenger-type apparatus. The antioxidant activity was evaluated by two methods: the scavenging of the free radical DPPH, and the reduction in iron. Anti-inflammatory activity was evaluated by evaluating the edema development induced by carrageenan injecting, while the analgesic power was evaluated according to the number of abdominal contortions induced by the intraperitoneal injection of acetic acid (0.7%). The acute oral toxicity was performed to assess the potential toxicity of the studied EOs, followed by an analysis of the blood biochemical parameters. The results of the two antioxidant tests indicated that our extract mixture exhibits good iron reduction capacity and very interesting DPPH free radical scavenging power, with an IC₅₀ of around 4.38 ± 0.98 μg/mL higher than that of the benchmark antioxidant, BHT. The anti-inflammatory test demonstrated that the mixture administered orally at a dose of 150 mg/kg has a better activity, exceeding that of 1% Diclofenac, with a percentage of maximum inhibition of the edema of 89.99 ± 4.08. The number of cramps in the mice treated with the mixture at a dose of 150 mg/kg is significantly lower (29.80 ± 1.92) than those of the group treated with Tramadol (42.00 ± 2.70), respectively. The toxicity results show no signs of toxicity with an LD₅₀ greater than 150 mg/Kg. These interesting results show that the two plants’ EOs had an important anti-inflammatory, analgesic, and antioxidant activity, and also a powerful synergistic effect, which encourages further in-depth investigations on their pharmacological proprieties.     

Phytochemical Analysis,Antispasmodic, Myorelaxant,and Antioxidant Effect of Dysphania ambrosioides (L.) Mosyakin and Clemants Flower Hydroethanolic Extracts and Its Chloroform and Ethyl Acetate Fractions

Dysphania ambrosioides (L.) Mosyakin and Clemants is an annual or ephemeral perennial herb used traditionally in the Mediterranean region in folk medicine to treat various illnesses, including those related to the digestive system. This study aims to assess the antispasmodic, myorelaxant, and antioxidant effects of D. ambrosioides flower hydroethanolic extract and its chloroform and ethyl acetate fractions in a comparative study to evaluate the result of the extraction type on the potential activity of the extract. Both rat and rabbit jejunum were used to evaluate the antispasmodic and myorelaxant effect, while the antioxidant effect was evaluated using DPPH, a ferric reducing power assay, and a beta-carotene bleaching test. LC/MS-MS analysis was carried out to reveal the composition of the different types of extract. Following the results, the hydroethanolic extract showed a significant myorelaxant effect (IC₅₀ = 0.39 ± 0.01 mg/mL). Moreover, it was shown that the hydroethanolic extract demonstrated the best antispasmodic activity (IC₅₀ = 0.51 ± 0.05 mg/mL), followed by the ethyl acetate (IC₅₀ = 4.05 ± 0.32 mg/mL) and chloroform (IC₅₀ = 4.34 ± 0.45 mg/mL) fractions. The antioxidant tests showed that the hydroethanolic extract demonstrated high antioxidant activity, followed by the ethyl acetate and chloroform fractions. The LC/MS-MS analysis indicates that the plant extract was rich in flavonoids, to which the extract activity has been attributed. This study supports the traditional use of this plant to treat digestive problems, especially those with spasms.