Every finite dimensional normed algebra is isomorphic to the finite direct product of  or , it is also proved these algebras are ultrasemiprime algebras. In this paper, the ultrasemiprime proof of the finite direct product of  and  is generalized to the finite direct product of any ultrasemiprime algebras.

المستخلص يهدف هذا البحث الى تجاوز مشكلة البعدية من خلال طرائق الانحدار اللامعلمي والتي تعمل على تقليل جذر متوسط الخطأ التربيعي (RMSE) , أذ تم  استعمال طريقة انحدار الاسقاطات المتلاحقة  (PPR)    ,والتي تعتبر احدى طرائق اختزال الابعاد التي تعمل على تجاوز مشكلة البعدية (curse of dimensionality) , وان طريقة (PPR) من التقنيات الاحصائية التي تهتم بأيجاد الاسقاطات الاكثر أهمية في البيانات المتعددة الابعاد , ومع ايجاد كل اسقاط

     Let n be a positive integer and  denotes the number of overpartition triples. In this note, we prove two identities modulo 16 and 32 for . We provide a new method to reprove a result of Lin Wang for completely determining and  modulo 16. Also, we find and prove an infinite family of congruences modulo 32 for . The new method relies on expanding the fourth power of the overpartition infinite product together with the help of Gauss' identity.

Since her early beginning in 1974 in her novel "Les armoires vides", Annie Ernaux writing about life in all its various aspects remained her main goal. This novel gave the earliest signals of what would happen later on in her literary career. Indeed, her works showed abilities of echoing reality, her sufferance and experiences via the use of simple and clear language. Add to this, her writings are to be viewed as an expression of deep felt journey, and a continuous search due to the consequent changes coming out of her identity.

    We try here to give an answer to the question about writing as to whether being, to Ernaux herself, a need for the search about her social and feminist identity, or a pure literary work

Hollow core photonic bandgap fibers provide a new geometry for the realization and enhancement of many nonlinear optical effects. Such fibers offer novel guidance and dispersion properties that provide an advantage over conventional fibers for various applications. Dispersion, which expresses the variation with wavelength of the guided-mode group velocity, is one of the most important properties of optical fibers. Photonic crystal fibers (PCFs) offer much larger flexibility than conventional fibers with respect to tailoring of the dispersion curve. This is partly due to the large refractive-index contrast available in the silica/air microstructures, and partly due to the possibility of making complex refractive-index structure over the fibe

For the premature termination of the contract is the creditor’s ability to request the termination of the contract due to the debtor’s breach of the execution date based on the debtor’s explicitness not to perform upon the occurrence of this date or because of a presumption proving that breach. Or return it to the extent of the creditor’s ability to prove what he claims, and thus the burden of proof falls on the creditor.

There is no difficulty in proving the debtor's declaration of non-performance, but the difficulty lies in proving the perceived breach in the future, that is, the creditor concludes earlier on the date of implementation that the debtor will breach his obligation and therefore the creditor does not obtain

Public utilities are the most important institutions at the present time, because of their great importance in providing daily services to citizens to meet their needs, and thus help the state to develop and progress in various social, economic and even security fields, and they also have a major role in creating an environment filled with stability and good life.

Due to the great importance of public utilities, the hand of the legislator extended to protecting and regulating them in many legal texts, so he singled out many texts for them, whether in regulatory or even penal laws, and because penal texts are the most important legal texts because of their great role in protection, as well as their connection to the rights and fre