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In this paper, we study a class of fractional p(x)-Laplacian Dirichlet problems in a bounded domain with Lipschitz boundary. Using variational methods, we prove in different situations the existence and multiplicity of solutions.

Combining bacterial metabolites and natural products of plants is one proposed alternative to antibiotic usage. Reports on such combinations are starting to emerge. This study aimed to determine the antibacterial potential of bacteriocin (BacLP01) produced by Lactobacillus plantarum and the essential oil of Rosmarinus officinalis L (ROEO) alone and their combination. Each antibacterial agent was tested against food-borne pathogens: Bacillus subtilis, Bacillus cereus, Escherichia coli, and Staphylococcus aureus using the agar well diffusion method. The antibacterial agents were evaluated from their minimum inhibitory concentration (MIC) against the test organisms. The checkerboard technique was performed to assess the resulting combination to determine the nature of the sum effects between antibacterial agents against B. subtilis ATCC11778. BacLP01 achieved the highest activity against B. subtilis, equivalent to 6400 AU/mL. ROEO showed an inhibition zone ranging from 10.23 ± 1.92 to 14.52 ± 0.83mm. S. aureus expressed the highest sensitivity to ROEO (14.52 ± 0.83 mm), and B. subilis presented low susceptibility with a 10.23± 1.92 mm diameter inhibition zone. Likewise, the synergistic effect of their combination on B. subilis ATCC11778 follows the same trend. The MICs for bacteriocin (BacLP01) and ROEO were 5 and 6.25 µL/mL, respectively. The result from FICI for the combination of BacLP01 and ROEO was 0.49, suggesting a synergistic interaction effect against B. subtilis. The study concluded that a combination of BacLP01 and ROEO could be an efficient means to control the presence of pathogenic bacteria in food. [ABSTRACT FROM AUTHOR]

We compared the characteristics of the 13 patients with CNS involvement (CNS+) with 62 patients without evidence of active CNS disease (CNS-). B Introduction: b Central nervous system (CNS) involvement in patients with refractory or relapsed large B-cell lymphoma (LBCL) is associated with an extremely poor prognosis. Treatment with anti CD19 CAR-T cells is safe and effective in patients with relapsed refractory large B-cell lymphoma with active central nervous system involvement. [Extracted from the article]

In this paper, a quasilinear elliptic system involving a pair of (p,q)-Laplacian operators with Steklov boundary value conditions is studied. Using the Mountain Pass Geometry, we prove the existence of at least one weak solution. For the infinitely many weak solutions, we based on Bratsch’s Fountain Theorem.

In this paper, we study the existence and non-existence of a weak solutions to the following system: $$\left\{ \begin{array}{ll} \Delta_p u=\Delta_q v=0& \mbox{ in }\Omega\\ |\nabla u|^{p-2}\frac{\partial u}{\partial \nu}=\lambda m|u|^{p-2} u-\varepsilon[(\alpha+1)|u|^{\alpha-1}u |v|^{\beta+1}-f] & \mbox{ on }\partial\Omega\\ |\nabla v|^{q-2}\frac{\partial v}{\partial \nu}=\lambda n|v|^{q-2} v-\varepsilon[(\beta+1)|v|^{\beta-1}v |u|^{\alpha+1}-g] \mbox{ on } \partial\Omega, \end{array} \right.$$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$ $(N\geq2)$ with a smooth boundary $\partial\Omega$, $\Delta_pu=\mbox{div}(|\nabla u|^{p-2}\nabla u)$ is the p-Laplacian, $\frac{\partial}{\partial\nu}$ is the outer normal derivative, $\varepsilon\in\{0, 1\}$, $ m, n$, $f$ and $g$ are functions that satisfy some conditions.

We study the existence and non-existence of positive solutions for $(p,q)$-Laplacian Steklov problem with two parameters. The main result of our research is the construction of a continuous curve in plane, which becomes a threshold between the existence and non-existence of positive solutions.

Objective: To design a whole-body MR protocol using exclusively diffusion-weighted imaging (DWI) with respiratory gating and to assess its value for lesion detection and staging in patients with diffuse large B-cell lymphoma (DLBCL), with integrated FDG PET/CT as the reference standard.Methods: Fifteen patients underwent both whole-body DWI (b = 50, 400, 800 s/mm(2)) and PET/CT for pretreatment staging. Lymph node and organ involvement were evaluated by qualitative and quantitative image analysis, including measurement of the mean apparent diffusion coefficient (ADC).Results: A total of 296 lymph node regions in the 15 patients were analysed. Based on International Working Group size criteria alone, DWI findings matched PET/CT findings in 277 regions (94%) (kappa score = 0.85, P < 0.0001), yielding sensitivity and specificity for DWI lymph node involvement detection of 90% and 94%. Combining visual ADC analysis with size measurement increased DWI specificity to 100% with 81% sensitivity. For organ involvement, the two techniques agreed in all 20 recorded organs (100%). All involved organ lesions showed restricted diffusion. Ann Arbor stages agreed in 14 (93%) of the 15 patients.Conclusion: Whole-body DWI with ADC analysis can potentially be used for lesion detection and staging in patients with DLBCL. [ABSTRACT FROM AUTHOR]

Cytarabine ocfosfate (YNK01) is a prodrug analogue of cytarabine which is resistant to systemic deamination after oral administration. Following initial studies indicating significant anti-tumour activity of YNK01 a phase II trial was initiated in order to assess the tolerability and efficacy of a combination of this agent with interferon alpha-2b (IFN-alpha2b) in recently diagnosed chronic phase CML patients (n = 98). The treatment was subdivided into cycles consisting of 4 weeks of continuous administration of IFN-alpha-2b (3 MU/m(2)/day 1st week and then 5 MU/m(2)/day) and 14 days of oral YNK01 (600 mg/day 1st cycle). At the end of each cycle the dose of YNK01 was adjusted according to the blood count observed during the previous 4 weeks. The median time from diagnosis to inclusion in the trial was 2 months (range 6 days to 7.5 months). At 12 weeks, 62 patients (63%; 95% CI, 54-73) achieved a complete hematological response. At 24 weeks, of 98 patients, two achieved a complete cytogenetic response, 14 a partial response (16% major cytogenetic response rate; 95% CI, 9-24) and 34 a minor response; 19 patients were not evaluable for cytogenetic response. During the trial, 20 patients progressed to accelerated (6) or blastic phases (14). The median time to progression was 15 months (range 2-38 months). At 3 years the overall survival was 79% (95% CI, 70-88). Although the complete hematological response rate compared favorably with the 40% response rate previously obtained with the subcutaneous formulation of Ara-c, the cytogenetic response rate was less than expected. Most of the patients experienced side-effects and all permanently stopped YNK01. Although the combination seems attractive the initial dose of 600 mg per day is probably too high and should be reconsidered in further trials. [ABSTRACT FROM AUTHOR]

In the presentp aper, we study the existence and non-existence results of a positive solution for the Steklov eigenvalue problem driven by nonhomogeneous operator $(p,q)$-Laplacian with indefinite weights. We also prove that in the case where $\mu>0$ and with $10$ there exists an interval of principal eigenvalues for our Steklov eigenvalue problem.

We use the Hardy-Sobolev inequality to study existence and non-existence results for a positive solution of the quasilinear elliptic problem -\Delta{p}u − \mu \Delta{q}u = \limda[mp(x)|u|p−2u + \mu mq(x)|u|q−2u] in \Omega driven by nonhomogeneous operator (p, q)-Laplacian with singular weights under the Dirichlet boundary condition. We also prove that in the case where μ > 0 and with 1 < q < p < \infinity the results are completely different from those for the usual eigenvalue for the problem p-Laplacian with singular weight under the Dirichlet boundary condition, which is retrieved when μ = 0. Precisely, we show that when μ > 0 there exists an interval of eigenvalues for our eigenvalue problem.

Using variational methods, we prove in a different cases the existence and multiplicity of $a$-harmonic solutions for the following elleptic problem:\begin{equation*}\begin{gathered}div(a(x, \nabla u))=0, \quad \text{in }\Omega, \\a(x, \nabla u).\nu=f(x,u), \quad \text{on } \partial\Omega,\end{gathered}\end{equation*} where $\Omega\subset\mathbb{R}^N(N \geq 2)$ is a bounded domain ofsmooth boundary $\partial\Omega$ and $\nu$ is the outward normalvector on $\partial\Omega$. $f: \partial\Omega\times \mathbb{R} \rightarrow \mathbb{R},$ $a: \overline{\Omega}\times \mathbb{R}^{N} \rightarrow\mathbb{R}^{N},$ are fulfilling appropriate conditions.

By applaying the Ricceri's three critical points theorem, we show the existence of at least three solutions to the following elleptic problem: \begin{equation*} \begin{gathered} -div[a(x, \nabla u)]+|u|^{p(x)-2}u=\lambda f(x,u), \quad \text{in }\Omega, \\ a(x, \nabla u).\nu=\mu g(x,u), \quad \text{on } \partial\Omega, \end{gathered} \end{equation*} where $\lambda$, $\mu \in \mathbb{R}^{+},$ $\Omega\subset\mathbb{R}^N(N \geq 2)$ is a bounded domain of smooth boundary $\partial\Omega$ and $\nu$ is the outward normal vector on $\partial\Omega$. $p: \overline{\Omega} \mapsto \mathbb{R}$, $a: \overline{\Omega}\times \mathbb{R}^{N} \mapsto \mathbb{R}^{N},$ $f: \Omega\times\mathbb{R} \mapsto \mathbb{R}$ and $g:\partial\Omega\times\mathbb{R} \mapsto \mathbb{R}$ are fulfilling appropriate conditions.

By applying two versions of Mountain Pass Theorem, we prove two different situations of the existence of solutions for the following Steklov problem $\Delta_{p(x)}u =|u|^{p(x)-2}u$ in $\Omega$, $|\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu}= \lambda |u|^{q(x)-2}u$ on $\partial\Omega$, where $\Omega$ is a bounded domain in $\mathbb{R}^{N}(N\geq 2)$ with smooth boundary $\partial\Omega$ and $p(.), q(.):\bar{\Omega}\rightarrow (1, +\infty)$ are continuous functions.

In this paper we prove the existence of a weak solution to the following system△_p u = △_q v = 0 in Ω,|∇u|^{p−2} ∂_ν u = f(x,u) − (α + 1)K(x)|u|^{α−1}u|v|^{β+1} + f1 on ∂Ω,|∇v|^{q−2} ∂_ν v = g(x,v) − (β + 1)K(x)|v|^{β−1}v|u|^{α+1} + g1 on ∂Ω,where Ω is a bounded domain in RN (N ≥ 2), f1, g1, f, g and K are functions that satisfy some conditions.

In this paper, we show the existence of a sequences of eigenvalues for an operator homogenous at the infinity, we give his variational formulation and we establish the simplicity of all eigenvalues in the case N = 1. Finally we study thesolvability of the problemA(u) := −div(A(x,∇u)) = f(x, u) + h in Ω,u = 0 on ∂Ω,as well as the spectrum ofG_0'(u) = λm|u|^{p−2}u in Ω,u = 0 on ∂Ω.

In this paper, we prove the existence of weak solutions to the problem △_p u = 0 in Ω, |∇u|^{p−2} ∂_ν u = λ_1 m(x)|u|^{p−2}u + f(x, u) − h on ∂Ω, where Ω is a bounded domain in RN (N ≥ 2), m ∈ L^q(∂Ω) is a weight, λ_1 is the first positive eigenvalue for the eigenvalue Steklov problem △pu = 0 in Ω and |∇u|^{p−2} ∂_ν u=λ m(x)|u|^{p−2}u on ∂Ω. f and h are functions that satisfy some conditions.

abstract: In this paper, we give some properties of the first nonprincipal eigenvalue for an asymmetric Steklov problem with weights, and we study the Fucik spectrum.

In this article, we study the existence of the eigencurves for a Steklov problem and we obtain their variational formulation. Also we prove the simplicity and the isolation results of each point of the principal eigencurve. Also we obtain the continuity and the differentiability of the principal eigencurve.

In this paper we prove existence and uniqueness of classical solutions for the non-autonomous inhomogeneous Cauchy problem $$displaylines{ frac{d}{dt}u(t)=A(t)u(t)+f(t), quad 0 leq sleq tleq T, cr L(t)u(t)=Phi(t)u(t)+g(t) , quad 0leq sleq tleq T, cr u(s)=x. }$$ The solution to this problem is obtained by a variation of constants formula.

Les 3 principaux types d'amylose cardiaque sont la conséquence de dépôts organiques de deux précurseurs protéiques : d'une part l'amylose AL (AL), secondaire à des dépôts de chaînes légères d'immunoglobulines dans le cadre d'une gammapathie monoclonale (essentiellement de signification indéterminée ou d'un myélome), et d'autre part les amyloses à transthyrétine (ATTR), comprenant les amyloses à transthyrétine sauvages et les amyloses à transthyrétine héréditaires. La fréquence de ces maladies est probablement sous-estimée, comme le montrent les études récentes sur sa prévalence élevée dans des phénotypes cardiologiques courants (insuffisance cardiaque à fraction d'éjection préservée, rétrécissement aortique serré, cardiomyopathie hypertrophique). L'infiltration amyloïde myocardique concerne toutes les structures cardiaques et peut conduire à la survenue d'une insuffisance cardiaque, de troubles conductifs et d'évènements cardio-emboliques. La recherche des signes extracardiaques est une aide au diagnostic. L'électrocardiogramme, l'échocardiographie et l'IRM cardiaque permettent de suspecter l'amylose cardiaque. La confirmation diagnostique se fait sur l'application d'un algorithme simple incluant une recherche systématique de gammapathie monoclonale par un bilan protéique complet et une scintigraphie aux disphosphonates (traceur osseux DPD, HMDP, PyP). Une documentation histologique est impérative en cas d'AL ; elle sera également requise en cas d'ATTR s'il existe une immunoglobuline monoclonale et/ou un ratio anormal de chaînes légères afin d'initier le traitement spécifique. Compte tenu de l'âge tardif d'apparition de la maladie dans les formes héréditaires, la réalisation d'un test génétique est systématique en cas d'ATTR. Ces maladies n'étant plus perçues comme incurables depuis les récentes innovations thérapeutiques, une meilleure (re)connaissance de la maladie est plus que jamais nécessaire. The 3 main types of cardiac amyloidosis are linked to two protein precursors: AL amyloidosis secondary to free light chain deposits in the context of monoclonal gammopathy (mainly of undetermined significance or myeloma) and transthyretin amyloidosis (ATTR), comprising wild-type transthyretin amyloidosis (ATTRwt for wild type) and hereditary transthyretin amyloidosis (ATTRv for variant). These diseases are underdiagnosed and highly prevalent in common cardiac phenotypes in recent studies (heart failure with preserved ejection fraction, severe aortic stenosis, hypertrophic cardiomyopathy). Myocardial amyloid infiltration affects all cardiac structures and clinically promotes predominantly heart failure, conductive disorders and cardioembolic events. The search for extracardiac signs makes it possible to arouse diagnostic suspicion. Electrocardiogram, echocardiography and cardiac MRI can suspect cardiac amyloidosis. The diagnostic confirmation follows a simple algorithm including a systematic search for monoclonal gammapathy and a disphosphonate scintigraphy. Histological proof is necessary in case of AL or ATTR amyloidosis with concomitant monoclonal gammopathy in order to initiate specific treatment. Due to the late disease onset in ATTRv, genetic testing must be routine in all cases of ATTR. These diseases are no longer perceived as incurable since recent therapeutic innovations. A better knowledge of the disease is more than ever necessary. [ABSTRACT FROM AUTHOR]