Multiple Solutions on a Ball for a Generalized Lane Emden Equation

In this work we study the Generalized Lane-Emden equation and the interplay between the exponents involved and their consequences on the existence and non existence of radial solutions on a unit ball in n dimensions. We extend the analysis to the phase plane for a clear understanding of the behavior of solutions and the relationship between their existence and the growth of nonlinear terms, where we investigate the critical exponent p and a sub-critical exponent, which we refer to as ^p. We discover a structural change of solutions due the existence of this sub-critical exponent which we relate to the same change in behavior of the Lane- Emden equation solutions, for ; = 0; andp = 2, due to the same sub-critical exponent. We hypothesize that this sub-critical exponent may be related to a weighted trace embedding

The Effect of Promotion Mix Elements on Consumers Buying Decisions of Mobile Service: The case of Umniah Telecommunication Company at Zarqa city- Jordan

This research aims to study the factors affecting the consumers buying decisions of mobile service provided by Umniah Telecommunications Company in Zarqa city; the factors include advertising, personal selling, sales promotion, and public relations. Data were collected through questionnaires forming a representative sample. A total of 440 questionnaires were distributed to Umniah Telecommunication Company consumers in Zarqa city, the findings indicated that there is a positive effect of  advertising, personal selling, sales promotion, and public relations with consumers buying decisions. Advertising was found to be the most critical factor in affecting consumers buying decisions. Keywords: promotion mix, advertising, personal selling, sales promotion, public relations, consumers buying decisions, Jorda

Territorial relationship marketing: a lever of territorial attractiveness

The attractiveness of the territory is a strategic objective of public policies. This objective is explained by the contribution of Foreign Direct Investments (FDI) to economic growth and even to the sustainable development of the host country. Nevertheless, the frenzy of competition between territories on a global scale combined with a galloping globalization and the fragmentation of value chains on an international scale highlights the need to go beyond the promotion of location factors Multinational Firms (MNCs) providers of FDI. Inexorably, the factors of territorialization become significant in a context punctuated by the growing nomadism of foreign companies. It is in this context that this work focuses on the need to adopt a relational approach to promote the economic attractiveness of the territory. This approach, which involves the implementation of a relationship marketing strategy, has demonstrated its effectiveness in maintaining lasting and fruitful relationships with customers in both B to B and B to C. This effectiveness relational marketing involves the mobilization of its determining variables, which are fully addressed by several theories such as the theory of commitment / trust and relational contracts. Our research work seeks to broaden the scope of relationship marketing in order to question its ability to establish lasting and fruitful relationships with FDI. Therefore, the establishment of such relationships is important for the host territory insofar as it is no longer the attractiveness of FMNs carrying FDI that is dominant. We must also strive to retain the latter, increase the capital intensity of subsidiaries and even strengthen their local roots. This said anchoring is able to contribute to the territorial development of the host country.     Classification JEL : F21, F23, M31 Article type: Theoretical articleL’attractivité du territoire est un objectif stratégique des politiques publiques. Cet objectif est expliqué par la contribution des Investissements Directs à l’Étranger (IDE) à la croissance économique et même au développement durable du pays d’accueil.  Néanmoins, la frénésie de la concurrence entre les territoires à l’échelle mondiale combinée à une globalisation galopante et à la fragmentation des chaînes de valeur à l’échelle internationale met en exergue la nécessité d’aller au-delà de la promotion des facteurs de localisation des Firmes Multinationales (FMN) pourvoyeuses des IDE. Inexorablement, les facteurs de territorialisation deviennent prégnants dans un contexte scandé par le nomadisme croissant des entreprises étrangères. C’est dans ce contexte que le présent travail se focalise sur la nécessité d’adopter une approche relationnelle pour favoriser l’attractivité économique du territoire. Cette approche, qui passe par la mise en place d’une stratégie de marketing relationnel, a démontré son efficacité quant à l’entretien de relations durables et fructueuses avec les clients tant dans le B to B que dans le B to C. Cette efficacité du marketing relationnel passe par la mobilisation de ses variables déterminantes amplement abordées par plusieurs théories à l’instar de la théorie de l’engagement/ confiance et celle des contrats relationnels.  Notre travail de recherche cherche à élargir le champ d’application du marketing relationnel pour ainsi interroger sa capacité, à établir des relations durables et fructueuses avec les IDE. Ipso facto, l’établissement de telles relations est important pour le territoire d’accueil dans la mesure où ce n’est plus l’attractivité des FMN porteuses d’IDE qui est dominante. Il faut aussi tendre vers la rétention de ces dernières, l’augmentation de l’intensité capitalistique des filiales et même le renforcement de leur ancrage territorial. Cedit ancrage est à même de contribuer au développement territorial du pays d’accueil.     Classification JEL: F21, F23, M31 Type de l’article : Article théoriqu

In-line broadband 270 degrees (3 lambda/4) chevron four-reflection wave retarders

The net differential phase shift Δt introduced between the orthogonal p and s linear polarizations after four successive total internal reflections inside an in-line chevron dual-Fresnel-rhomb retarder is a function of the first internal angle of incidence φ and prism refractive index n. Retardance of 3λ/4 (i.e., Δt=270°) is achieved with minimum angular sensitivity when φ=45° and n=1.900822. Several optical glasses with this refractive index are identified. For Schott glass SF66 the deviation of Δt from 270° is ≤4° over a wavelength range of 0.55≤λ≤1.1 μm in the visible and near-IR spectrum. For a SiC prism, whose totally reflecting surfaces are coated with an optically thick MgF2 film, Δt=270° at two wavelengths: λ1=0.707 μm and λ2=4.129 μm. This coated prism has a maximum retardance error of ≈5°over\u3ethree octaves (0.5 to 4.5μm) in the visible, near-, and mid-IR spectral range. Another mid-IR 3λ/4 retarder uses a Si prism, which is coated by an optically thick silicon oxynitride film of the proper composition, to achieve retardance that differs from 270° by \u3c0.5° over the 3-5 μm spectral range

Polarization properties of retroreflecting right-angle prisms

The cumulative retardance Δt introduced between the p and the s orthogonal linear polarizations after two successive total internal reflections (TIRs) inside a right-angle prism at complementary angles Φ and 90°−Φ is calculated as a function of Φ and prism refractive index n. Quarter-wave retardation (QWR) is obtained on retroreflection with minimum angular sensitivity when n=(√2+1)1/2=1.55377 and Φ=45°. A QWR prism made of N-BAK4 Schott glass (n=1.55377 at λ=1303.5 nm) has good spectral response (\u3c5° retardance error) over the 0.5-2 μm visible and near-IR spectral range. A ZnS-coated right-angle Si prism achieves QWR with an error of \u3c±2.5° in the 9-11 μm (CO2 laser) IR spectral range. This device functions as a linear-to-circular polarization transformer and can be tuned to exact QWR at any desired wavelength (within a given range) by tilting the prism by a small angle around Φ=45°. A PbTe right-angle prism introduces near-half-wave retardation (near-HWR) with a ≤2% error over a broad (4≤λ≤12.5 μm) IR spectral range. This device also has a wide field of view and its interesting polarization properties are discussed. A compact (aspect ratio of 2), in-line, HWR is described that uses a chevron dual Fresnel rhomb with four TIRs at the same angle Φ=45°. Finally, a useful algorithm is presented that transforms a three-term Sellmeier dispersion relation of a transparent optical material to an equivalent cubic equation that can be solved for the wavelengths at which the refractive index assumes any desired value

Broadband IR polarizing beam splitter using a subwavelength-structured one-dimensional photonic-crystal layer embedded in a high-index prism

An iterative procedure for the design of a polarizing beam splitter (PBS) that uses a form-birefringent, subwavelength-structured, one-dimensional photonic-crystal layer (SWS 1-D PCL) embedded in a high-index cubical prism is presented. The PBS is based on index matching and total transmission for the p polarization and total internal reflection for the s polarization at the prism-PCL interface at 45 degrees angle of incidence. A high extinction ratio in reflection (\u3e50 dB) over the 4-12 mu m IR spectral range is achieved using a SWS 1-D PCL of ZnTe embedded in a ZnS cube within an external field of view of +/- 6.6 degrees and in the presence of grating filling factor errors of up to +/- 10%. Comparable results, but with wider field of view, are also obtained with a Ge PCL embedded in a Si prism

In-line broadband 270 degrees (3 lambda/4) chevron four-reflection wave retarders

The net differential phase shift Δt introduced between the orthogonal p and s linear polarizations after four successive total internal reflections inside an in-line chevron dual-Fresnel-rhomb retarder is a function of the first internal angle of incidence φ and prism refractive index n. Retardance of 3λ/4 (i.e., Δt=270°) is achieved with minimum angular sensitivity when φ=45° and n=1.900822. Several optical glasses with this refractive index are identified. For Schott glass SF66 the deviation of Δt from 270° is ≤4° over a wavelength range of 0.55≤λ≤1.1 μm in the visible and near-IR spectrum. For a SiC prism, whose totally reflecting surfaces are coated with an optically thick MgF2 film, Δt=270° at two wavelengths: λ1=0.707 μm and λ2=4.129 μm. This coated prism has a maximum retardance error of ≈5°over\u3ethree octaves (0.5 to 4.5μm) in the visible, near-, and mid-IR spectral range. Another mid-IR 3λ/4 retarder uses a Si prism, which is coated by an optically thick silicon oxynitride film of the proper composition, to achieve retardance that differs from 270° by \u3c0.5° over the 3-5 μm spectral range

ENHANCEMENT OF DISSOLUTION AND STABILITY OF CANDESARTAN CILEXETIL–LOADED SILICA POLYMERS

Objective: To prepare stable amorphous solid dispersions of candesartan cilexetil (CAN) with different types of silica, including non-porous (aerosil 200) and porous silica (sylysia 350) using the spray-drying method. Methods: various ratios of candesartan cilexetil (CAN) were spray dried with aerosil and sylysia. Powder x-ray diffraction (x-ray) differential scanning calorimetry (DSC), SEM were used to characterize the spray dried powders in addition to dissolution and stability studies. Results: X-ray results showed that the spray–dried (CAN) in the prepared solid dispersion were in amorphous form irrespective of the used silica. In (DSC) analysis, the melting peak of spray-dried (CAN-silica) solid dispersion disappeared. Dissolution property of (CAN) was remarkably improved by formulating with silica particles. In comparing the effect of the type of the silica particles, the dissolution rate of (CAN) from the spray-dried (CAN-sylysia) was faster than that (CAN-aerosil 200) irrespective of the drug content. It was also shown that the spray-dried formulation with silica did not recrystallize when storing at severe storage conditions (40 °C, 75% RH) for three months, while spray-dried (CAN) without silica easily re-crystallized under the same conditions. Conclusion: Spray drying of (CAN) with sylysia 350 is an efficient method to enhance the dissolution and stability of the drug

Broadband IR polarizing beam splitter using a subwavelength-structured one-dimensional photonic-crystal layer embedded in a high-index prism

An iterative procedure for the design of a polarizing beam splitter (PBS) that uses a form-birefringent, subwavelength-structured, one-dimensional photonic-crystal layer (SWS 1-D PCL) embedded in a high-index cubical prism is presented. The PBS is based on index matching and total transmission for the p polarization and total internal reflection for the s polarization at the prism-PCL interface at 45 degrees angle of incidence. A high extinction ratio in reflection (\u3e50 dB) over the 4-12 mu m IR spectral range is achieved using a SWS 1-D PCL of ZnTe embedded in a ZnS cube within an external field of view of +/- 6.6 degrees and in the presence of grating filling factor errors of up to +/- 10%. Comparable results, but with wider field of view, are also obtained with a Ge PCL embedded in a Si prism