In this paper, there are two competitors in a planar market. The first competitor, called, the leader, opens p new facilities. After that, the second competitor, the follower, reacts to the leader's action and opens r new facilities. The leader and the follower have got some facilities in advance in this market. The optimal locations for leader and follower are chosen among predefined candidate locations. In this paper, it is assumed that the demand is inelastic. Considering the huff model, customers share their demand among all facilities, probabilistically. The leader's objective function is the maximization of its market share after the follower's new facilities entry. The leader and follower problems are solved via an exact solution method.

Please click on PDF to view the abstract.

Let X be a reflexive Banach space, T: X®X a nonexpansive mapping with C=Fix (T)  ¹ Æ; and F: X®X d-strongly accretive and l-strictly pseudocontractive with d+l>1. In this paper, we present modified hybrid steepest-descent methods involving Sequential and functional errors with functions admitting a center which generate convergent sequences to the unique solution of the variational inequality V I* (F, C). We also present similar results for a strongly monotone and Lipschitzian operator in the context of a Hilbert space and apply the results for solving a minimization problem.

Let $X$ be a Hausdorff locally convex topological vector space with $\Omega $ and $X^{*}$ as its topology and Topological dual respectively. Suppose $f:[0,1]\rightarrow X$ is a function defined on $X$ and $\rho(X)$, a family of $\rho$-continuous seminorms on $X$ such that the topology is generated by $\rho(X)$. Is f Sequential Mcshane(SMcS) and Sequential Henstock(SH) integrable with respect to the semi-norm on time scale? Do these integrals coincide and relate to other integrals such as Pettis and Bochner for which the Sequential Henstock lemma holds for the characterization of locally Convex space on time scale? It is the purpose of this paper to give affirmative answers to these questions.

Background & Aim: Dental plaque is recognized as the main etiologic factor in gingival diseases. There fore, prevention and control of plaque aggregation on various dental surface display a very significant role in prophylaxis and treatment of both gingivitis and periodontitis. However mechanical removing of the plaque is the primary method for dental and oral hygiene, It can not be carried out perfectly even by precision patient. To resolve the problem, it is recommended to add chemical control to mechanical method. In respect to the importance of chemical control, this study purposes to evaluate synergic effect and compare effect of chlorhexidine, NaF mouth washes, a type of chemical method, on plaque control.Materials & Methods: The studied group consist of 15 dentistry students. After a thorough professional prophylaxis including interdental cleaning.15 subjects started to rinse according to 4 different regiments: regimen CH-NaF: chlorhexidine Immediately followed by Sodium fluoride in the morning and in the evening; regimen NaF-CH: Sodium Fluoride immediately followed by Chlorhexidine in the morning and in the evening; regimen CH: chlorhexidine in the morning and in the evening; regimen NaF: Sodium Fluoride in the morning and in the evening. No further oral hygiene measures were allowed for the next 5 day. After 5day, the subject were scored for BOP, PI and PCR, afther of days’ washout period of 4 days. Following this procedure, all subjects went through all 4 regiments.Results: Our observation revealed no bleeding due to probing in all who used four rinsing regimes. The rate of plaque index varied according to the type and manner of the mouthwash applied, so that minimal plaque index was seen in combining chlorhexidine / Sodium Fluoride regimen. In addition, the mean plaque control record percent different in accordance to the type and manner of the mouthwash applied, so that the lowest mean was illustrated in the regimen combining chlorhexidine / Sodium Fluoride mouthwashes.Conclusion: The observation showed no bleeding on probing in subjects who applied four regimens. The best outcomes of plaque index and plaque control record were obtained with use of chlorhexidine-sodium fluoride mouth washes.

A review of various legal rules comprising the law of obligations in the Iranian legal system demonstrates that this system recognizes a special type of obligations with the unusual property that its burden is neither on one specific person (individual responsibility), nor on several persons simultaneously (joint responsibility), but, in two or more subsequent stages, along a specified priority, on different persons, so that in each stage, the creditor's claim is due to be paid from a different person’s property. The creditor could pass to the next stage only when in the previous, there has been found no, or insufficient, assets. The obligations of involved persons, in other words, cover each other alternatively. The type of obligation thus described has not been viewed as a genuine, independent one in the Iranian legal system so far. Rather, it is considered as a special and exceptional phenomenon, or even as an irregularity. Therefore, the instances fitting in this type have not been collected and studied together, its constituting elements have not been specifically studied, and the rules governing it have not been formulated. This article is intended to study this type of responsibility as a genuine and independent type among obligations and to examine its instances, elements and the rules governing it. The method of this research is descriptive and analytical. Accordingly, in the beginning, the article will descriptively review various laws that contain, or constitute an application of, the Sequential responsibility, either explicitly or implicitly. Then, in the analytical phase, an attempt will be made to derive the general principles, elements and rules governing the provisions embodied in that particular body of law. In this way, the most important interpretive instrument will be the induction from various legal provisions. The library research method will also be employed. The hypothesis of this research is that the Sequential responsibility is not exceptional or irregular, but a genuine, purposeful and regular type which the legislator is able to use when necessary. It is a combination of the individual and the joint responsibility, aiming to support both the debtor and the creditor at the same time. Also, it can be conceived as a form of insurance for a number of obligations, each backed by the obligation(s) of the next stage. Therefore, by coherent explanation and analysis of the rules governing this type of responsibility, the scope of its appropriate application can be suggested to the legislator and to the legal doctrine. The principal questions of this research are: 1. what are the examples of Sequential responsibility in the Iranian laws? 2. What are the structural characteristics and the elements of this type and its differences with other types of responsibility? 3. What general rules governing this type could be induced and to what issues could they be applied? On the other hand, the following hypotheses will be suggested: 1. The hierarchy between the liabilities of different persons for paying alimony to relatives, as well as the sequence in paying the blood money between a) Aqila (paternal relative of the felon), b) the felon, and c) the public treasury are prime examples of this type of responsibility. Also, the sequence between a) minor's liability and b) its culpable guardian's liability, and in some cases, the liabilities of a) the company director and shareholders/members, and b) the company/legal entity should be considered as examples of this type of liability, 2. The elements of this type of responsibility are: Sequentiality, single debt, and multiple properties. 3. There are general rules governing matters such as: the aim of responsibility, the relationship between liable persons, and the scope of responsibility. This article has depicted as a regular category a group of obligations that have always been viewed as sporadic or exceptional cases. The article will present them as an independent, original institution in the Iranian law, with the proposed name "Sequential liability". Various instances of this type of liability will be traced through different laws and put together as a coherent category. These include: Sequential liability between the invalid (the insane and the minors) and their culpable guardian (Article 7 of the Civil Liability Act), Sequential responsibility between different persons for paying alimony to their relatives (Articles 1198 et seq. of the Civil Code), Sequential responsibility between the director of a legal entity and the entity itself to compensate for damages caused by a crime (Article 28 of the Protection of Authors, Writers and Artists Act, legislated in 1970), Sequential liability between limited liability and general partnership companies and their partners/shareholders (Articles 126, 186 and 187 of the Commercial Code), Sequential liability between the company and its culpable director against third parties (Article 143 of the Amendment to the Commercial Code), and Sequential responsibility between the Aqila (paternal relative of the felon), the felon, and the public treasury, to pay blood money (Articles 470, 435, 471, 474 and 475 of the Islamic Penal Code). Instead of focusing on divergences, the article will explore similarities and common elements in various cases, as is necessary in any scientific research. Common elements are: a) Sequentiality, which means the Sequential relation between a number of obligations based on a specified priority, b) multiple properties, meaning that Sequential responsibility shifts, at each level, from one liable person’s property, to the property of the person in the next rank, c) one debt, meaning that the content of obligation is the same for all Sequential ranks, bearing same qualitative and quantitative characteristics. Finally, by induction from various bodies of law, and by taking into account the purpose and the rationale behind this type of responsibility, the general rules governing it, which are applicable in similar cases or when no specific rule can be found in the texts, will be formulated as follows: first, the aim of Sequential liability is to support both the creditor and the debtor, in that the creditor will have access to multiple properties to collect the debt, and the debtor will not be forced to face hardship by fulfilling the debt. Thus, this is a genuine category of responsibilities, along with the individual and the joint responsibility, second, as to the relationship between Sequential debtors, since each of them is paying his own debt, he cannot, in principle, claim against those in the previous or the next rank to refund what he has paid, such as is the case for the one who pays the relative’s alimony, third, the scope of Sequential responsibility, in accordance with its rationale and its premises, is that each debtor in any rank is responsible for all of the debt, and only the portion he failed to pay will be transferred to the next rank. As for the case where several debtors are in the same rank, the rule is that each will have to pay an equal share of the debt.

It is henceforth a commonplace; the science-fiction would be a refractory genre by nature against the definitive assimilation to the literary mainstream. We can say that the usual thematic of the genre, to which is added the irresistible propensity to prospect the future in all its forms, immunizes the SF against the “academic confinement” to the benefit of other forms of confinement. Indeed, the SF belongs to the great family of the paraliterature where the more or less listed subgenres are waiting to receive a likely definition. Popular genre which relies on a remarkable poetic, the SF is an open place to the imagination, to the verbal and the figurative creativity. It owns itself its subgenres, among other things, the space opera which was, in a way, the original matrix of the speculative fiction and of its contemporary imitators. The Sternberg’s work did not have a special vocation to feed the already rich world of the science-fiction. It constitutes however a new step liable to bring a touch of self-reflexivity, we will notice that, to the history of this genre. French: “Le Navigateur” de Jacques Sternberg ou la phylogenese parodiee du space opera C’est dorenavant un lieu commun, la science-fiction serait un genre par nature refractaire a l’assimilation definitive au mainstream litteraire. Nous dirons que les thematiques habituelles du genre, auxquelles viennent se meler l’irresistible propension a prospecter l’avenir sous toutes ses formes, immunisent la SF contre “l’enfermement academique” au profit d’un enfermement d’un autre genre. En effet, celle-ci appartient, comme on le sait, a la grande famille de la paralitterature ou se cotoient les sous-genres plus ou moins repertories en attente de recevoir un semblant de definition. Genre populaire s’appuyant sur une poetique singuliere, la SF est un lieu ouvert a l’imagination, a la creativite verbale et figurative. Elle possede elle-meme ses sous-genres, entre autres, le space opera qui fut en quelque sorte la matrice originelle de la fiction speculative et de ses emules contemporaines. L’oeuvre sternbergienne n’eut guere pour vocation de nourrir le repertoire deja riche de la science-fiction. Elle constitue neanmoins une etape non repertoriee susceptible d’apporter, nous le constaterons, une touche d’auto-reflexivite a l’histoire du genre.Keywords: Jacques Sternberg, Nouvelle, Science-Fiction, space Opera, Aventure, Fiction Speculative