Perturbation analysis in a free boundary problem arising in tumor growth model

We study the existence and multiplicity of solutions of the following free boundary problem (P)\left\{ \begin{array}{rcll} \del u &=& \lam ( \eps +(1-\eps ) H(u-\mu))~ \hspace{3mm}&\text{in}~\Omega (t)\\ u&=& \overline{u}_{\infty}~\hspace{3mm} &\text{on } ~ \partial \Omega(t) \end{array} \right. where \Omega(t) \subset \RR^3 a regular domain at $t>0$, \eps,~\overline{u}_{\infty},~\lambda,~\mu are a positive parameters and $H$ is the Heaviside step function. \\The problem (P) has two free boundaries: the outer boundary of $\Omega(t)$ and the inner boundary whose evolution is implicit generated by the discontinuous nonlinearity $H$. The problem (P) arise in tumor growth models as well as in other contexts such as climatology. First, we show the existence and multiplicity of radial solutions of problem (P) where $\Omega(t)$ is a spherical domain. Moreover, the bifurcation diagrams are giving. Secondly, using the perturbation technic combining to local methods, we prove the existence of solutions and characterize the free boundaries of problem (P) near the corresponding radial solutions

A note on discontinuous problem with a free boundary

AbstractWe study a nonlinear elliptic problem with discontinuous nonlinearity(P)-Δu=f(u)H(μ-u)inΩ,u=0on∂Ω,where H is the Heaviside’s unit function, f, h are given functions and μ is a positive real parameter. We prove the existence of a unique solution and characterize the corresponding free boundary. Our methods relies on variational inequality approach combining with fixed point arguments

SITUATION OF BRUCELLOSIS IN CATTLE FARMS IN A PASTORAL REGION OF ALGERIA (DJELFA) AND ITS IMPACT ON PUBLIC HEALTH: AN EXAMPLE OF DETECTION OF BRUCELLA ORGANISM IN FERMENTED RAW COW MILK « L’BEN »

Brucellosis is an infectious disease that spreads to humans and causes major economic loss. In addition, it poses a public health problem in Algeria and in many countries. In order to assess the situation of this disease in the region of Djelfa (Algeria) and to estimate its risk on public health, a study was extended from 2010 to 2018. In addition, it is accompanied by bacteriological analyzes on samples of "L’ben" fermented milk taken from certain outlets in the same region to find out the importance of brucellosis, as an infectious disease, as well as the risks to the health of consumers . The results showed that out of a total of 287640 cattle, only 4.42% were screened with a reported prevalence of seropositive cattle of 2.51%. In addition, the prevalence of bovine brucellosis varied from year to year. It was low in 2010 with 07 reported cases (0.67%), while it was high in 2016 with 57 reported cases (4.18%). In addition, for human brucellosis, the prevalence varies between 4.3% in 2013 and 20.25% in 2018, with an average of 11.11%. In parallel, the results of laboratory analysis have shown that the average prevalence rate of brucella spp in fermented milk "L’ben" was 77.78% and that the highest rate was observed in Messaad (100%) and Hassi Bahbah (100%). While the lowest rate was reported in Dar Chioukh (33.33%). These results reflect the risk posed to cattle by brucellosis, especially on public health, and the risk posed by the consumption of  brucellosis-contaminated L’ben. This necessitates the implementation of a disease control and awareness program in order to avoid various accidents and significant economic losses. In addition, the early diagnosis of the disease helps preserve the health of the consumer thereafter

Cezayir, Bejaia'daki mezbaha verilerine dayanan tüberküloz hakkında i̇lk rapor: Geriye dönük 10 yıllık bir araştırma

Tuberculosis (TB) is a widespread and endemic disease of ruminants in Algeria posing a significant threat to public health. A retrospective abattoir study was conducted in Bejaia province (Algeria) from 2009 to 2018 to estimate the prevalence of tuberculosis in cattle, sheep, and goats using detailed meat inspection procedure. The overall prevalence of tuberculosis was 2.06% (4092/199 077) in cattle, 0.007% (11/168 796) in sheep, and 0.008% (11/164 986) in goats. The annual prevalence rate of the disease showed intermittent increase in levels over the ten years period of the study. However, monthly fluctuations of tuberculous lesions in slaughtered cattle were recorded throughout the study period with detection rates ranging from 1.77% and 2.36%. In addition, the variation in seasonal prevalence in cattle and goats is not significant (P > 0.05). Our analysis has revealed the magnitude of TB in the study area and warrants further systematic investigation on the transmission of the disease in Algeria.Tüberküloz (TB), Cezayir'de halk sağlığı için önemli bir tehdit oluşturan ruminantların yaygın ve endemik bir hastalığıdır. Bejaia'da (Cezayir) sığır eti, koyun ve keçilerde tüberküloz prevalansının ayrıntılı bir et muayene prosedürü kullanılarak tahmin edilmesi için geriye dönük bir mezbaha çalışması yapılmıştır. Tüberküloz prevalansı sığırlarda % 2.06 (2.092/199 077), koyunlarda % 0.007 (11/168 796) ve keçilerde % 0.008 (11/164 986) idi. Hastalığın yıllık yaygınlık oranı, çalışmanın on yıllık dönemi boyunca aralıklarla artmıştır. Ancak, kesilen sığırlarda aylık tüberküloz lezyonlarındaki dalgalanmalar, çalışma süresi boyunca % 1.77 ile % 2.36 arasında değişen tespit oranlarında kaydedilmiştir. Ayrıca sığır ve keçilerde mevsimsel prevalanstaki değişiklik anlamlı değildir (P> 0.05). Analizimiz, çalışma alanındaki TB'nin büyüklüğünü ortaya çıkarmıştır ve Cezayir'de hastalığın bulaşmasına ilişkin daha fazla sistematik araştırmayı garanti etmektedir

iNaturalist: aplicaciones, oportunidades y aspectos a tener en cuenta en cuanto a su uso en botánica

Comunicación oral presentada en el XI Congreso de Biología de la Conservación de Plantas (SEBiCoP) celebrado del 17 al 21 de julio de 202

Perturbation of the free boundary in elliptic problem with discontinuities

We study the discontinuous elliptic problem \displaylines{ -\Delta u = \lambda H(u-\mu ) \quad \text{in } \Omega,\cr u =h \quad \text{on }\partial \Omega, } where $\Omega$ is a regular bounded domain of $\mathbb{R}^n$, $H$ is the Heaviside function, $\lambda, \mu$ are a positive real parameters and h is a given function. We prove the existence of solutions, and characterize the free boundaries $\{x\in \Omega: u(x)=\mu\}$ using the perturbation of the boundary condition and smooth boundary of the domain

An in-store experiment: How shelf position (central vs. extremes) affects buying tendency of customers.

Important prior studies regarding customers purchasing behaviour proved that customers tend to avoid products showing extreme deflections in attributes and feel more comfortable purchasing articles with a balance in attributes (compromise option). Hence, for marketers, supermarket chains etc., it can be of an advantage knowing whether this effect can also be measured or even be amplified in where the spatial middle of a shelf is occupied with the compromise option. We hypothesized that the tendency towards the compromise option, eventually even higher in the spatial middle position, can also be observed in an in-store experiment with real-life circumstances. In order to fulfil our study, we worked with a hardware store in southern Germany. In total, we sold 610 items consisting of 5 different products with each 3 alternatives. The result corroborated our hypothesis partly as it showed in some cases, the compromise option was indeed preferred when in the middle of a choice set. Nevertheless, in many cases, products on extreme position with “extreme” attributes were preferred. Leading to the conclusion that other factors like the brand may have higher importance in purchasing decisions

The teaching-learning of the grammar of FLE in Algeria, case of complex sentences by propositional subordination. Subordinate proposals and their ranking

This research attempted  to question the different metalinguistic discourses that can  account  for the  construction modalities of complex sentences by propositional subordination. For this, we presented a reassessment and a confrontation of the various points of view on the question. This critical examination has allowed us to identify a grid of analysis that offers for each of the specimens studied the synthesis of its defining features, but also divergences and ambiguities that surround it. Along the way, we have seen how most notions of the system suffer from axioms inherited from the grammatical tradition and hide poor vague and fluctuating conceptual content. This detailed study allowed us to analyze the various teaching aids in order to evaluate the teaching of complex sentences by propositional subordination, and to evaluate the competences of learners from the educational system in question at the level of complex sentences by subordination. propositional