Combinatorial Results for Semigroups of Order-Preserving Full Transformations

Let O_n be the semigroup of all order-preserving full transformations of a finite chain, say X_n = {1, 2, ..., n}, and for a given full transformation α: X_n → X_n let f(α) = |{x ∈ X_n: xα = x}|. In this note we obtain and discuss formulae for f(n,r,k) = |{α → O_n: f(α) = r ∧ max(Im α) = k}| and J(n,r,k) = |{α → O_n: |Im α| = r ∧ max(Im α) = k}|. We also obtain similar results for E(O_n), the set of idempotents of O_n.     

A time-dependent external-field model for particle emission in heavy-ion reactions

We study a time-dependent external-field model for fast particle emission in nuclear heavy-ion reactions. The relative motion of the ions is treated classically and the internal excitations are treated quantum mechanically. The model is applied to study fast nucleon emission in the reaction ¹⁶O + ⁹³Nb.     

A new phthalic acid ester from Ajuga bracteosa

A new phthalic acid ester 1,2-benzenedicarboxylic acid bis(2S-methyl heptyl) ester (1) was isolated from the hexane extract of the whole plant of Ajuga bracteosa. In addition, chloroform and methanol extracts yielded neo-clerodane diterpene ajugarin-I and two iridoid glycosides, reptoside and 8-O-acetyl harpagide. The structures of all the compounds were confirmed by extensive spectroscopic analysis. From the two oily fractions nine and six volatile constituents respectively were identified by GCMS. Linalyl acetate was found to be common in both the oil fractions. This plant is a new source of linalyl acetate, a valuable perfumery compound.     

Interacting Entropy-Corrected Holographic Chaplygin Gas Model

Holographic dark energy (HDE), presents a dynamical view of dark energy which is consistent with the observational data and has a solid theoretical background. Its definition follows from the entropy-area relation S(A), where S and A are entropy and area respectively. In the framework of loop quantum gravity, a modified definition of HDE called “entropy-corrected holographic dark energy” (ECHDE) has been proposed recently to explain dark energy with the help of quantum corrections to the entropy-area relation. Using this new definition, we establish a correspondence between modified variable Chaplygin gas, new modified Chaplygin gas and the viscous generalized Chaplygin gas with the entropy corrected holographic dark energy and reconstruct the corresponding scalar potentials which describe the dynamics of the scalar field.     

Role of ion energy flux on the structural and morphological properties of silicon oxy-nitride composite films deposited by plasma focus device

ABSTRACT

Crystalline silicon oxy-nitride (SiON) composite films are deposited on Si substrate for multiple (5, 15, 25 and 50) focus shots (FS) by plasma focus device. The X-rays diffraction patterns reveal the development of various diffraction peaks related to Si, Si₃N₄, and SiO₂ phases which confirms the formation of SiON composite film. The intensity of Si₃N₄ (1 0 2) plane is linearly increased with the increase of FS. The Si₃N₄ (1 0 2) phase does not nucleate for 5 FS. Raman analysis confirms the formation of β–Si–N phase. Raman and Fourier transform infrared spectroscopy analysis reveals that the strength of chemical bonds like Si–N, Si–O formed during the deposition process of SiON composite films is associated with the bonds intensity which in turn depends on the number of FS. The field emission scanning electron microscopic analysis reveals that the surface morphology like size, shape and distribution of micro/nano-dimensional particles, film compactness and the formation of micro-rods, micro-teethes and micro-tubes of SiON composite films is entirely associated with the rise in substrate surface transient temperature which in turn depends on the increasing number of FS. The EDX spectrum confirms the presence of Si (22.5?±?4.7 at. %), N (13.4?±?4.5 at. %) and O (54.7?±?11.3 at. %) in the SiON composite film. The thickness of SiON composite film deposited for 50 FS is found to ～15.47?µm.     

Presentation for the Partial Dual Symmetric Inverse Monoid

We give a monoid presentation in terms of generators and define relations for the partial analogue of the finite dual symmetric inverse monoid.     

Elemental Analysis of Cement by Calibration-Free Laser Induced Breakdown Spectroscopy (CF-LIBS) and Comparison with Laser Ablation – Time-of-Flight – Mass Spectrometry (LA-TOF-MS), Energy Dispersive X-Ray Spectrometry (EDX), X-Ray Fluorescence Spectroscopy (XRF), and Proton Induced X-Ray Emission Spectrometry (PIXE)

The purpose of the present study is to determine the elemental composition of Pakistani cement brands using calibration-free laser induced breakdown spectroscopy (CF-LIBS) and to compare the obtained results with the other analytical techniques such as, laser ablation – time-of-flight – mass spectrometry (LA-TOF-MS), energy dispersive X-ray spectrometry (EDX), X-ray fluorescence spectroscopy (XRF) and proton induced X-ray emission spectrometry (PIXE). Compositional results reveal that all the cement brands are mainly composed of calcium, silicon, iron, aluminum, magnesium, potassium, sodium, titanium, lithium and strontium with varying concentrations. The compositions obtained by LIBS and LA-TOF-MS are in good agreement with results obtained by the other standard techniques and demonstrate the potential use of LIBS for the online monitoring of industrial cement production.     

Structural Evolution and Electronic Properties of Au2Gen-/0 (n=1-8) Clusters: Anion Photoelectron Spectroscopy and Theoretical Calculations

Investigating the structures and properties of Au-Ge mixed clusters can give insight into the microscopic mechanisms in gold-catalyzed Ge films and can also provide valuable information for the production of germanium-based functional materials. In this work, size-selected anion photoelectron spectroscopy and theoretical calculations were used to explore the structural evolution and electronic properties of Au₂Ge_n^-/0 (n=1-8) clusters. It is found that the two Au atoms in Au₂Ge_n^-/0 (n=1-8) showed high coordination numbers and weak aurophilic interactions. The global minima of Au₂Ge_n^- anions and Au₂Ge_n neutrals are in spin doublet and singlet states, respectively. Au₂Ge_n^- anions and Au₂Ge_n neutrals showed similar structural features, except for Au₂Ge₄^-/0 and Au₂Ge₅^-/0. The C_2v symmetric V-shaped structure is observed for Au₂Ge₁^-/0, while Au₂Ge₂^-/0 has a C_2v symmetric dibridged structure. Au₂Ge₃^-/0 can be viewed as the two Au atoms attached to different Ge-Ge bonds of Ge₃ triangle. Au₂Ge₄^- has two Au atoms edge-capping Ge₄ tetrahedron, while Au₂Ge₄ neutral adopts a C_2v symmetric double Au atoms face-capping Ge₄ rhombus. Au₂Ge_5-8^-/0 show triangular, tetragonal, and pentagonal prism-based geometries. Au₂Ge₆ adopts a C_2v symmetric tetragonal prism structure and exhibits σ plus π double bonding characters.