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Мы исследуем существование, ограниченность, асимптотику и колебательное поведение положительных решений нечеткого разностного уравнения $$ z_{n+1}=A+\frac{B}{z_{n-m}} , $$ где $n\in\mathbb{N}_{0}=\mathbb{N}\cup\{0\}$, $(z_{n})$ - последовательность положительных нечетких чисел, $A$, $B$ и начальные условия $z_{-j}$, $j=1,2,…,m$, - положительные нечеткие числа, а $m$ - целое положительное число. Библиография: 27 названий.

In this paper, a new mathematical model that describes the dynamics of the within-host COVID-19 epidemic is formulated. We show the stochastic dynamics of Target-Latent-Infected-Virus free within the human body with discrete delay and noise. Positivity and uniqueness of the solutions are established. Our study shows the extinction and persistence of the disease inside the human body through the stability analysis of the disease-free equilibrium $$E_0$$ E 0 and the endemic equilibrium $$E^*$$ E ∗ , respectively. Moreover, we show the impact of delay tactics and noise on the extinction of the disease. The most interesting result is even if the deterministic system is inevitably pandemic at a specific point, extinction will become possible in the stochastic version of our model.

A discrete-time predator–prey model is investigated in this paper. In considered model, the population is assumed to follow the model suggested by Ricker 1954. Existence and stability of equilibria are studied. Numerical simulations reveal that, depending on the parameters, the system has complicated and rich dynamics and can exhibit complex patterns. Also the bifurcation diagrams are presented.

A strong and healthy microbiome is responsible for homeostasis between the host and microbiota which is necessary to achieve the normal functioning of the body. Dysbiosis provokes prevalence of pathogenic microbes, leading to alterations in gene expression profiles and metabolic processes. This in turn results in anomalous immune responses of the host. Dysbiosis may be associated with a wide variety of diseases like irritable bowel syndrome, coeliac disease, allergic conditions, bronchitis, asthma, heart diseases and oncogenesis. Presently, the links between oral microbial consortia and their functions, not only in the preservation of homeostasis but also pathogenesis of several malignancies have gained much awareness from the scientific community. The primary intent of this review is to highlight the dynamic role of oral microbiome in oncogenesis and its progression through various mechanisms. A literature search was conducted using multiple databases comprising of PubMed, Scopus, Google Scholar, and Cochrane electronic databases with keywords including microbiome, microbiota, carcinogenesis, tumorigenesis, and immunosuppression. Current and the past literature has pointed out the role of microorganisms in oncogenesis. It may be put forth that both the commensal and pathogenic strains of oral microbiome play an undeniably conspicuous role in carcinogenesis at different body sites.

In this paper, a new stochastic mathematical model for the spread of COVID-19 is formulated. First, we show the well-posedness of the proposed new stochastic mathematical model, then we investigate the stochastic dynamics of the spread of this virus in the sense of the mean-square. Conditions of extinction and persistence are obtained. Some numerical simulations are performed to strengthen the theoretical results. The sensitivity of the model with respect to the parameters involved in the system is shown to investigate the most sensitive parameter toward the highest number of infected individuals. The results reveal the mechanisms that influence the transmission and control of the disease besides the prediction and this, in turn, will be very useful for understanding the pattern of COVID-19 and other epidemic models.

In this paper, we explore local stability, attractor, periodicity character, and boundedness solutions of the second-order nonlinear difference equation. Finally, obtained results are verified numerically.

The scope of dentistry is ever-changing and dynamic in all fields of dentistry including periodontal health and disease. Recent studies show that oral health and systemic health are interdependent, particularly in the way that poor oral hygiene and periodontal health affect the systemic health of an individual and vice versa. Periodontal diseases are multifactorial in nature in which the role of bacterial infections is inevitable. Furthermore, high-throughput sequencing technologies have shed light on the dysregulation of the growth of oral microbial flora and their environment, including those that are associated with periodontitis and other oral and non-oral diseases. Under such circumstances, it becomes important to explore oral microbiota and understand the effects of periodontal pathogens in the pathogenesis of systemic diseases. In addition, it may strengthen our view that a better understanding of oral microbial flora and proper examination of the oral cavity may aid in the early diagnosis and possible treatment of systemic diseases and conditions. This will eventually lead to providing better care to our patients. Therefore, in this research, we attempt to outline the periodontal pathophysiology along with the role of periodontal pathogens in some commonly encountered systemic conditions.

IntroductionHepatitis C virus (HCV) is the main cause of chronic liver disease, with calamitous complications. Its highest rate is recorded in Egypt. This study investigated whether oxidative stress, immunological chaos and cellular hypoxia are implicated in the pathophysiology of the disease.Material and methodsThis cross-sectional study aimed to evaluate the changes in blood oxidative stress, cellular hypoxia/angiogenesis and cellular immunological biomarkers in hospital-diagnosed treatment-naïve HCV-infected Upper Egyptian chronic liver disease patients vs. healthy controls (n = 40). The consecutively included patients comprised 120 with normal serum enzymes (HCV-NE) and 130 with high serum enzymes (HCV-HE), along with 120 cirrhotic patients.ResultsOxidative stress biomarkers – malondialdehyde (MDA), total peroxides and oxidative stress index (OSI) – were significantly lower in controls vs. each of the patient groups. Cirrhotic patients presented the highest levels. However, total antioxidants (TAO) showed non-significant differences among the four groups. The cellular hypoxia/angiogenesis biomarkers – lactate, vascular endothelial cell growth factor (VEGF) and its soluble receptor 1 (sVEGFR1) – vs. controls were massively increased in patient groups. VEGF was lowest while sVEGFR1 was highest among cirrhotic patients. Immunological biomarkers, – granulocyte/monocyte-colony stimulating factor (GM-CSF) and total immunoglobulin G (IgG) – were massively increased in patient groups vs. controls. GM-CSF was lowest in HCV-HE and IgG was highest in cirrhotic patients. sVEGFR1 correlated with the progression towards cirrhosis.ConclusionsOxidative stress is implicated in the progress of HCV infection with marked induction of cellular hypoxia and dysfunctional angiogenesis, and a futile immunological reaction. sVEGFR1 level correlated with progression towards HCV-induced liver fibrosis.

(1) Backgrounds and Objectives: Since its discovery, information about the severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) has spread rapidly. However, many issues remain unresolved. Coronaviruses are primarily transmitted through respiratory secretions. The possibility of transmission via donated blood transfusion deserves studying. This is the first study in Saudi Arabia to look at pre-vaccination donated blood anti-SARS-CoV-2 antibody content as a marker for virus transmission via viral RNA positive blood and/or the potential therapeutic value of convalescent plasma. (2) Methods: A total of 300 blood samples were sequentially collected from unvaccinated donors who donated blood to the blood bank of Prince Mutaib Bin Abdulaziz Hospital in Sakaka, Al-Jouf, Saudi Arabia. Specific ELISA was used to detect anti-SARS-CoV-2 IgG and IgM antibodies. SARS-CoV-2 was detected using specific real-time reverse-transcription PCR (rRT-PCR). (3) Results: The prevalence of anti-SARS-CoV-2 IgG was low (9%), whereas the prevalence of anti-SARS-CoV-2 IgM was high (65%). Relevant demographics, anthropometrics, and lifestyle factors revealed significant associations (p < 0.05) between IgM-positivity only vs. age (age group 21–30 years), postgraduate education, no history of international travel, IgG-negativity, and absence of experience with COVID-19-like symptoms. Furthermore, there are significant associations (p < 0.05) between IgG-positivity only vs. age (age group 21–30 years), postgraduate education, and being a non-healthcare worker. All donors in the anti-SARS-CoV-2 IgG-positive group (n = 27) had previously experienced symptoms similar to COVID-19 (p < 0.001) and most of them (n = 24) showed anti-SARS-CoV-2 IgM-positive test (p = 0.006). However, all the samples tested negative for SARS-CoV-2 RNA using rRT-PCR. (4) Conclusion: Our findings add to the growing body of evidence that donated blood is safe, with the added benefit of convalescent plasma rich in potentially neutralizing IgG and IgM against SARS-CoV-2.

Vitamin D (VitD) deficiency during pregnancy has been associated with adverse neonatal outcomes and increased risk of late pregnancy complications. We planned to correlate serum VitD biomarkers; 25-hydroxyvitamin D (25-OH-VitD) and 1,25-dihydroxyvitamin D (1,25-diOH-VitD) levels; and their ratio with the frequency of feto-maternal pregnancy complications. A prospective cross-sectional case-control study was conducted at Aljouf Maternity and Children Hospital, Sakaka, Saudi Arabia, during the period of September 1, 2017 to September 30, 2019. 322 pregnant women were stratified into 2 groups: controls (110 cases) and complicated group (212 cases). The later comprised severe preeclamptic toxemia associated with intrauterine growth restriction (58 cases), gestational diabetes mellitus (GDM; 82 cases), abortion (26 cases), undisturbed ectopic pregnancy (16 cases), premature rupture of membranes (PROM; 14 cases), and, inevitable preterm labour (16 cases). After clinical assessment, peripheral blood samples were collected. Serum biomarkers were measured using specific immunoassays. The direct 1,25-diOH-VitD/25-OH-VitD ratio was calculated. Serum 25-OH-VitD indicated widely spreading VitD deficiency among participants with significantly higher levels in controls vs. GDM subgroup only. 1,25-diOH-VitD levels and the ratio were markedly reduced in the six complicated subgroups vs. controls, with non-significant differences amongst the complicated subgroups. ROC analysis showed very high sensitivity and specificity, to differentiate patients from controls, only for 1,25-diOH-VitD (AUC = 0.965; 0.947 - 0.983, p

(1) Backgrounds and Objectives: The global battle to contain the severe acute respiratory syndrome-coronavirus-2 (SARS-CoV-2) is still ongoing. This cross-sectional study aimed to detect the seroprevalence of anti-SARS-CoV-2 IgM/IgG among previously symptomatic/asymptomatic and vaccinated/unvaccinated inhabitants of Sakaka City, Aljouf, Saudi Arabia. (2) Methods: Blood samples of 400 participants were tested for the presence of anti-SARS-CoV-2 IgM/IgG using colloidal gold immuno-chromatography lateral flow immunoassay cards. (3) Results: The prevalence of anti-SARS-CoV-2 IgM and IgG positivity was 45.8% and 42.3%, respectively. Statistically significant correlations (p < 0.05) were found between the previous RT-PCR testing for SARS-CoV-2-RNA and positivity for IgM and/or IgG. The highest seroprevalence of IgM and IgG were detected among smokers, participants aged ≥40 years, and patients with chronic diseases. Although most of the participants (58.5%) did not previously experience COVID-19 like symptoms, the anti-SARS-CoV-2 IgM and IgG seropositivity amongst them was 49.1% and 25.6%, respectively, with higher seroprevalence among males than females. At the time of the study, the SARS-CoV-2 vaccination rate at our locality in Saudi Arabia was 43.8% with statistically significant correlation (p < 0.001) between being vaccinated and anti-SARS-CoV-2 IgM and/or IgG positivity, with more positivity after receiving the second vaccine dose. (4) Conclusions: Public assessment reflects the real scale of the disease exposure among the community and helps in identifying the asymptomatic carriers that constitute a major problem for controlling the SARS-CoV-2. To limit the spread of the virus, rigorous implementation of large-scale SARS-CoV-2 vaccination and anti-SARS-CoV-2 serological testing strategies should be empowered.

A healthy microbiome is important for human health because it exhibits a variety of functions in the human body wherein the microbiome dysbiosis can lead to a variety of diseases, including cancer. Recent advances in technology and cost reduction of sequencing have made it possible and much easier for researchers to investigate the role of the microbiome in carcinogenesis. Furthermore, modulation of microflora may serve as an effective adjunct to conventional anticancer therapy that is very important to improve the patient’s quality of life. Additionally, microbiome biomarkers can also be used as a diagnostic tool for cancer. So far the association between oral microbial consortia and their interactions with the host in maintaining the human health and the pathogenesis of multiple cancers has gained much popularity in the scientific research community. While the interactions of oral microflora are better established in cancer- like gastric cancer, it is far less understood in others like breast cancer. Therefore, this review briefly outlines the current information on the role of oral microbiota in breast cancer with emphasis on the mechanisms of oral microflora induced carcinogenesis and discusses the emerging role of periodontitis as a risk factor for breast cancer. Clinical relevance; Periodontitis is a very common disease that is characterized by chronic polymicrobial infection and inflammation of gingiva. It might be associated as a risk factor for breast cancer. If this association is validated in large cohort studies, it would serve as a non-invasive biomarker for breast cancer.

This manuscript is involved in the study of stability of the solutions of functional differential equations (FDEs) with random coefficients and/or stochastic terms. We focus on the study of different types of stability of random/stochastic functional systems, specifically, stochastic delay differential equations (SDDEs). Introducing appropriate Lyapunov functionals enables us to investigate the necessary conditions for stochastic stability, asymptotic stochastic stability, asymptotic mean square stability, mean square exponential stability, global exponential mean square stability, and practical uniform exponential stability. Some examples with numerical simulations are presented to strengthen the theoretical results. Using our theoretical study, important aspects of epidemiological and ecological mathematical models can be revealed. In ecology, the dynamics of Nicholson’s blowflies equation is studied. Conditions of stochastic stability and stochastic global exponential stability of the equilibrium point at which the blowflies become extinct are investigated. In finance, the dynamics of the Black–Scholes market model driven by a Brownian motion with random variable coefficients and time delay is also studied.

All-trans Retinoic acid (atRA) is instructive for the development of endocrine pancreas and is an integral component of β-cell induction protocols. We showed that atRA induces glucose-responsive endocrine transdifferentiation of pleomorphic pancreatic ductal adenocarcinoma cells in vitro. This study aimed to detect the role of atRA in improving the histological changes of the pancreas in diabetic rats. Forty young male Wistar rats were used and divided into three groups. Group I: normal vehicle control (N = 5). Group II: streptozotocin-induced diabetic rats (N = 20) were followed up at 0.0, 1, 2, and 4 weeks. Group III: streptozotocin-induced diabetic rats (N = 15) treated with atRA (2.5 mg/kg/day), were followed up at 1, 2, and 4 weeks. Specimens from the pancreas were processed for light, electron microscopy and pancreatic insulin mRNA expression. Blood samples were assayed for the levels of glucose, insulin, and total peroxides. In the atRA-treated group, the number of the islets and the islet area significantly increased. Strong insulin-immunoreactive endocrine-like cells were observed nearby the pancreatic acini and the interlobular ducts. Interestingly, insulin-positive cells seemed to arise from pancreatic acinar and ductal epithelium. Ultrastructurally, s-cells, acinar, and ductal cells restored their normal appearance. Pancreatic insulin mRNA and blood indices were almost normalized. AtRA improved the histological changes of the pancreas and the blood indices in diabetic rats.

Surgical removal of intact hydatid cyst is the most effective treatment for hydatid disease. Recurrence of hydatid cyst is mainly due to dissemination of protoscolices (PSCs) rich fluid during the surgical operation. Therefore, preoperative instillation of a scolicidal agent into the cyst is a common practice with adverse side effects of the used drugs. All-trans retinoic acid (atRA) is the physiological mediator of most of the functions of vitamin A, particularly as a cellular differentiation and apoptosis regulating factor. We hypothesized that instillation of atRA could provide an alternative safe scolicidal approach. We tested the scolicidal effects and ultrastructural changes imposed by atRA on human hydatid cyst PSCs in vitro. Freshly isolated hydatid cyst PSCs were subjected to atRA (at 16.7, 1.67, 0.167 µM and 16.7 nM/L). Changes in protoscolices viability (0.1% eosin exclusion) and morphology (scanning and transmission electron microscopy; SEM and TEM) were investigated. Dose-dependent PSCs death within few minutes to 7 days of exposure to atRA was observed. SEM demonstrated ultrastructural damages including rosteller disorganization, loss of hooks and distortion of hooks morphology. TEM revealed loss of the integrity of the internal tissues of PSCs, an increased vacuolization, formation of large lipid droplets in the distal cytoplasm and aberrant, rounded abnormally large sized mitochondria. atRA is a promising alternative to the available synthetic and chemical scolicidal agents. However, in vivo scolicidal activities of atRA and the possible side effects necessitate further studies. Key words: Hydatid cyst, protoscolices, retinoic acid, ultrastructure, scolicidal activity.

This study aimed to investigate the oxidative stress, hypoxia biomarkers, and circulating microparticles (MPs) in β thalassemia major. The study included 56 children with thalassemia and 46 healthy controls. Hypoxia biomarkers, oxidative stress biomarkers, and total plasma fragmented DNA (fDNA) were detected by the standard methods. The MPs were assessed by flow cytometry. Hypoxia and oxidative stress biomarkers, fDNA, and MPs were higher and total antioxidant capacity (TAC) was lower in patients with thalassemia than the controls. In splenectomized patients and those who had complications, vascular endothelial growth factor (VEGF), malondialdehyde, fDNA, endothelial, platelet, and activated platelet MP levels were higher while, TAC was lower than the nonsplenectomized patients. In conclusion, the increased tissue hypoxia, oxidative stress in β thalassemia, and its relationship with DNA damage and MPs release could explain many complications of thalassemia and may have therapeutic implications. The VEGF could serve as an important indicator for adequacy of blood transfusion in thalassemia.

We study some qualitative properties of the solutions of a system of difference equations, which describes an economic model. The study of the local stability of the equilibrium points is carried out. We give some important results of the invariant and the boundedness of the solutions to the considered system. The global convergence of the solutions is presented and investigated.

We obtain in this paper the solutions of the following recursive sequences 𝑥 𝑛 + 1 = 𝑥 𝑛 𝑥 𝑛 − 3 / 𝑥 𝑛 − 2 ( ± 1 ± 𝑥 𝑛 𝑥 𝑛 − 3 ) , 𝑛 = 0 , 1 , … , where the initial conditions are arbitrary real numbers and we study the behaviors of the solutions and we obtained the equilibrium points of the considered equations. Some qualitative behavior of the solutions such as the boundedness, the global stability, and the periodicity character of the solutions in each case have been studied. We presented some numerical examples by giving some numerical values for the initial values and the coefficients of each case. Some figures have been given to explain the behavior of the obtained solutions in the case of numerical examples by using the mathematical program Mathematica to confirm the obtained results.

We present sufficient conditions which guarantee that all positive solutions of some higher order rational difference equations are global asymptotically stable. The boundedness of the solutions and the existence of prime period two solutions of such equations are also investigated.

In this paper we investigate the global convergence result, boundedness and periodicity of solutions of the recursive sequence \[ x_{n+1}=\frac{a_{0}x_{n}+a_{1}x_{n-1}+\dots +a_{k}x_{n-k}}{b_{0}x_{n}+b_{1}x_{n-1}+\dots +b_{k}x_{n-k}},\,\,\,n=0,1,\dots \,\ \] where the parameters $ a_{i}$ and $b_{i}$ for $i=0,1,\dots ,k$ are positive real numbers and the initial conditions $x_{-k},x_{-k+1},\dots ,x_{0}$ are arbitrary positive numbers.

In this paper, we consider the discrete nonlinear delay population model exhibiting the Allee effect (*) $$x_{n + 1} = x_n \exp \left( {a + bx_{n - \tau }^p - cx_{n - \tau }^q } \right),$$ where a, b and c are constants and p, q and τ are positive integers. First, we study the local stability of the equilibrium points. Next, we establish some oscillation results of nonlinear delay difference equations with positive and negative coefficients and apply them to investigate the oscillatory character of all positive solutions of equation (*) about the positive steady state x * and prove that every nonoscillatory solution tends to x *.

Background Non-alcoholic fatty liver disease (NAFLD) is a multifactorial disease with a complex pathophysiology. The clinical features of NAFLD include obesity, insulin resistance (IR) and dyslipidemia. Consumption of a diet high in saturated fats and sucrose is an important factor in the increasing occurrence of these metabolic disorders, primarily NAFLD and IR. We sought to assess the role of a high-fat, high-sucrose (HFS) diet in the promotion of NAFLD and to evaluate the effects of quercetin (Q), berberine (BB) and o-coumaric acid (CA) on modulation of these disorders. Methods Fifty male rats were divided into 2 main groups as follows: group 1 comprised 10 rats fed a standard diet (SD), and group 2 comprised 40 rats fed an HFS diet for 6 weeks and then subdivided equally into 4 groups; one of these groups served as the HFS diet and each of the other three groups received daily supplementation with either Q, CA or BB for 6 weeks. Results In the present study, several metabolic disorders were induced in our laboratory animal model, as evidenced by histological and biochemical changes. These alterations included serum and hepatic dyslipidemia (i.e., increased triglyceride, total cholesterol and low-density lipoprotein levels and decreased high-density lipoprotein levels), alterations in metabolic enzyme activities (lipase, glycerol-3-phosphate dehydrogenase, and glucose-6-phosphate dehydrogenase), histological changes in the liver (micro- and macrovesicular steatosis) and the downregulation of peroxisome proliferator-activated receptor γ (PPARγ) in adipose tissue and the liver. Daily oral supplementation with Q, CA or BB for 6 weeks after NAFLD induction had a hypolipidemic action and modulated metabolic markers. Conclusion We showed that an HFS diet is able to promote NAFLD, and our results suggest that CA and BB are promising complementary supplements that can ameliorate the metabolic disorders associated with an HFS diet; however, Q requires further investigation.

Background and hypothesis: The pancreatic ductal adenocarcinoma (HPAF) cells have a multipotent stem cell potential. It was hypothesised that all- trans -retinoic acid (atRA) can induce transdifferentiation of these cells into cells with an endocrine phenotype. Material and methods: To explore this hypothesis, an in vitro system of cells was established. Some cells were treated with atRA at concentrations of 100 nmol/l (non-apoptosis-inducing) and 5 μmol/l (apoptosis-inducing) and harvested. Cells were examined for cell cycle kinetics, apoptosis (terminal deoxynucleotidyl transferase assay and p53 protein expression) and immunomorphological features of redifferentiation (MUC1 and DUPAN-2) and endocrine transdifferentiation (insulin, somatostatin, glucagon, neurone-specific enolase) by using immunoperoxidase staining methods. Levels of insulin, transforming growth factor (TGF) β2, TGFα and epidermal growth factor receptor (EGFR) were measured by enzyme-linked immunosorbent assay (ELISA). The vehicle-treated cells served as a control group. Results: When compared with untreated cells, cells treated with 100 nmol/l and 5 μmol/l atRA were observed to show (1) decreased proliferative activity (cpm) as indicated by decreased incorporation of thymidine labelled with hydrogen-3; (2) cell cycle arrest; (3) increased apoptotic activity associated with p53 protein overexpression; (4) upregulated expression of the transdifferentiation and redifferentiation markers; (5) morphological changes indicative of transdifferentiation (increased cell size and appearance of dendrites); (6) decreased production of EGFR; (7) upregulation of TGFα and TGFβ 2 ; and (8) increase in basal and glucose-induced insulin secretion. Conclusions: Functional endocrine transdifferentiation can be induced in HPAF lines by atRA. Further investigations are mandated to explore the underlying mechanisms of this transdifferentiation and to explore its in vivo extrapolation.

Background: Our previous investigations showed that retinoids, at specific concentrations, can inhibit cell proliferation .In this investigation, we hypothesize that high concentrations of retinoids can induce phenotypic changes (differentiation) and late apoptosis in pancreatic cancer cells in vitro. Materials and methods: To test our hypothesis, retinoid-induced differentiation was assessed: 1) phenotypically by light and electron microscopy and 2) biochemically by measuring carbonic anhydrase, aerobic metabolic and mucin producing activities. Modulation of transforming growth factor –beta (TGF-_) and epidermal growth factor (EGF) autocrine pathways were utilized as mechanistic and differentiation markers. Results: The extensive differentiation-indicative phenotypic changes correlated with several folds increase in the aerobic metabolism (MTT reduction and Mitochondrial mass), carbonic anhydrase activity and mucin production. There was a marked increase in TGF-? (Bioassay and ELISA) and TGF-? (RIA) secr...

The anticancer ability of natural retinoids on pancreatic adenocarcinoma, an aggressive tumor, is still controversial. This investigation tested the hypothesis that all-trans retinoic acid can inhibit proliferation and induce apoptosis in pancreatic cancer cell lines.Using our previously optimized conditions, the effect of all-trans retinoic acid (atRA, 0.001-10 microM) was tested in ten human pancreatic adenocarcinoma cell lines with various degrees of differentiation. Proliferation was monitored by cell number, [3H]-thymidine incorporation and cell cycle arrest. Apoptosis was investigated morphologically by light and electron microscopy and biochemically by tissue transglutaminase activity (TGase), mitochondrial membrane potential, cell cycle analysis of sub-G1 cells and detection of fragmented DNA (fragmentation of prelabeled DNA, agarose electrophoresis and TUNEL assays).Retinoic acid caused potent concentration- and time-dependent inhibition of proliferation of all cell lines studied. Cell cycle was arrested at G1 or G2 with extensive reduction of number of cells at S-phase after 24 hours of treatment with apoptotic concentration of atRA. Complete inhibition of proliferation was followed by apoptosis as indicated by the progressive accumulation of sub-G1 apoptotic cells which was confirmed by the more specific DNA fragmentation assays. There were extensive apoptosis-indicative light and electron microscopic changes preceded by phenotypic redifferentiation. TGase was induced between 3-5-fold the control level and its inhibition partially reversed the antiproliferative effect of atRA. Cellular viability during the preapoptotic stage was confirmed by normal mitochondrial membrane potential in the first two days of treatment with the maximum atRA concentration used. However, the potential was progressively reduced with time as a preapoptotic change. Caspase 3-like activity was induced by the apoptotic concentrations of atRA at late time points. However, the redifferentiation indicative changes were not prevented by cotreatment with Ac-DEVE-CHO caspase 3 inhibitor.Together, our results demonstrated the efficient anticancer ability of natural retinoids on human pancreatic cancer cell lines tested, even those previously reported to be retinoid resistant.

We study some qualitative behavior of solutions of some max-type difference equations with periodic coefficients. Some new results of the periodicity character of solutions of that type of difference equations will be established.

BACKGROUND Secondary carnitine deficiency may develop in chronic renal failure (CRF) patients undergoing long-term hemodialysis (HD), with a resulting higher incidence of cardiovascular diseases, dyslipidemia and oxidative stress. We studied the efficacy of 12 months of L-carnitine supplementation on the amelioration of dyslipidemia, oxidative stress and cardiac dysfunction in 24 CRF children undergoing long-term HD compared with 24 age- and sex-matched controls. METHODS Plasma samples were analyzed spectrophotometerically before and after dialysis sessions and after 2-month supplementation with oral L-carnitine (50 mg/kg/day) for free carnitine (FC), the lipid profile, and oxidative stress markers. Echocardiography the day following dialysis measured cardiac diameters, wall thicknesses, left ventricular mass index (MI), end diastole and systole volume indices and functions. RESULTS The pre-dialysis FC concentration was substantially lower than controls and decreased significantly at the end of the dialysis session. Pre- and post-dialysis plasma levels of free fatty acids (FFAs), trigyleride (TG), total cholesterol (TC) and oxidative stress markers significantly increased while high-density lipoprotein cholesterol (HDL-C) and phospholipids significantly decreased compared to controls. Echocardiography detected a significant increase in cardiac diameters and thickness, and systolic and diastolic cardiac dysfunction. After L-carnitine supplementation, plasma levels of FC increased to normal levels. FFAs, TC and HDL-C returned to control levels while TG, phospholipids, and the oxidative stress markers decreased but remained significantly higher than controls. There was a significant decrease in cardiac diameters and an increase in left ventricular diastolic function (E/A ratio), but no correlation between FC levels and echocardiographic parameters. Pre-dialysis, post-dialysis and after treatment, plasma FC level showed a significant positive correlation with HDL-C and phospholipids and a significant negative correlation with each of oxidative stress markers, FFAs, TG and TC. On the other hand, FFAs showed a significant positive correlation with TG, TC, DC, NO and a significant negative correlation with HDL-C and phospholipids. CONCLUSION This study demonstrates that CRF children under regular HD suffer from a decrease in the level of plasma FC, dyslipidemia, oxidative stress, and an increase in cardiac diameters and thickness with impairment of cardiac functions. Oral L-carnitine supplementation at a dose of 50 mg/kg for 2 months can increase plasma FC level, improve dyslipidemia, decrease oxidative stress with reduction of cardiac diameters and increase in diastolic function.

We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument.