An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

In this paper, we find all solutions of the exponential Diophantine equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.Comment: Comments are welcom

Role of Estrogen Receptor Expression in Estrogen (E-2)-Induced Modulation of Th1 and Th2 Cytokine Responses

Previous studies have demonstrated that repeated administration of 17β-estradiol (E-2) at a dose of 1mg/kg to both (SWR x NZB)F1 (SNF1) mice and (DBA x BALB/c)F1(DBF1) mice resulted in significantly decreased survival and increased appearance of lupus nephritis pathology. However, the ways in which estrogen modulates immune responses has yet to be fully understood, specifically in regard to modulations in TH1 and TH2 cytokine profile. Various studies have reported the presence of two estrogen receptors (ER), a and b, which have been found to be constitutively expressed in many immune cells. In the present project, ER chimeric alpha knockout (αERKO), beta knockout (βERKO) and double knockout (αβERKO) as well as wild type(WT) mice were injected monthly with β-estradiol 17-valerate (E-2) at 1mg/kg. Control mice of each type received oil vehicle only. Results showed that TH1 cytokine production by cells from WT mice was suppressed by E-2 administration, although IFN-γ production was increased in cells from βERKO mice treated with estrogen compared to those treated with oil vehicle. TH2 cytokine production was increased in cells from WT mice treated with estrogen compared to controls. Increases in the production of anti-double stranded DNA antibodies were also observed in cells from αERKO mice. These observations suggest a role for differences in ER-α and ER-β expression in E-2 induced modulation of immune responses, including autoimmune diseases like Systemic Lupus Erythematosus (SLE)

Nonnegative integer solutions of the equation Ln(k)−Lm(k)=2×3αL_{n}^{(k)}- L_{m}^{(k)}=2\times 3^{\alpha }

For an integer k ≥ 2, let $\left (L_{n}^{(k)} \right )_{n}\geq -(k-2)$ be the k-generalized Lucas sequence, which starts with 0, ..., 0, 2, 1 (k terms) and each term afterwards is the sum of the k preceding terms. In 2019, Bitim found all the solutions of the Diophantine equation $L_{n}-L_{m}=2\cdot 3^{\alpha }$. In this paper, we generalize this result by considering the k-generalized Lucas sequence, i.e., we solve the Diophantine equation $L_{n}^{(k)}- L_{m}^{(k)}=2\times 3^{\alpha }$ in positive integers n, m, a with k ≥ 3. To obtain our main result, we use Baker’s method and the Baker-Davenport reduction method

On a variant of a Diophantine equation of Cassels

Recently, Yuan and Li considered a variant y2=px(Ax2-2) of Cassels\u27 equation y2=3x(x2+2). They proved that the equation has at most five solutions in positive integers (x, y). In this note, we improve Yuan-Li\u27s result by showing that for any prime p and any odd positive integer A, the Diophantine equation y2=px(Ax2-2) has at most three solutions in positive integers (x, y)

On the exponential Diophantine equation Pnx+P(xx+1)+...+P(xn+k−1)=PmP^x_n + P^x_(x+1) + ... + P^x_(n+k-1) = P_m

In this paper, we find all the solutions of the title Diophantine equation in positive integers (m, n, k, x), where P i is the i th term of the Pell sequenc

Cotton in Benin: governance and pest management

Key words: cotton, synthetic pesticides, neem oil (Azadirachta indica), Beauveria bassiana, Bacillus thuringiensis, field experiment, farmers’ participation Pests are one of the main factors limiting cotton production worldwide. Most of the pest control strategies in cotton production rely heavily on the application of synthetic pesticides. The recurrent use of synthetic pesticides has large consequences for the environment (air, water, fauna, and flora) and human health. In cotton growing areas in Benin, targeted pests develop resistance, and this resistance is extended to malaria mosquitos. Other negative impacts are pest resurgence and secondary pest outbreaks due to the effects on the beneficial insect fauna. This dissertation addresses the technical and institutional constraints hindering the wide-scale use of staggered targeted control, ‘Lutte étagée ciblée’ (LEC, in French) for cotton production. Wider adoption of LEC can only be achieved if some institutional changes were to occur, such as in the role of input suppliers in order to improve the procurement of LEC pesticides. This can only happen if farmers would be empowered and better organised. Locally available phytochemicals and biopesticides can be used to address problems related to the difficulty in obtaining synthetic pesticides, as well as their negative environmental impact. Neem oil (Azadirachta indica) and Beauveria bassiana are good candidates to be used in an integrated pest management approach, as their impact on the beneficial fauna is minimal. We tested whether the efficacy could be enhanced by using mixed formulations of neem oil and bio-insecticides, but yields obtained with neem oil used alone and mixed with biopesticides were not different. This suggests an absence of a synergistic effect between neem oil and B. bassiana (Bb11) and between neem oil and B. thuringiensis. The combination of biopesticides increased the cost of production more than that of the conventional treatments, compromising the profitability of such formulations. Participation in the research process increased farmers’ knowledge on pest and natural enemy recognition. The increase in knowledge did not lead to any modification in farmer practices with respect to the use of neem oil and Beauveria, but it led to a significant change towards threshold-based pesticide applications. Policy implications for successfully changing farming practices are discussed.</p

Restitution and return of looted royal heritage: the role of Ghanaian chiefs and queens in sustaining heritage traditions

In interrogating this discourse on the restitution and return of looted royal objects, ourrole and input in this conversation as traditional leaders in Ghanaian communities areinevitable. This is in the light of the fact that the source of most of these looted royalart objects unlawfully placed in German and some European museums are from theVolta Basin area of Ghana, formerly part of German Togoland. We argue that factoringin the views of chiefs and queens, being traditional leaders of communities inAfrica, provides a better understanding of the origin and contexts of the use of mostof these pirated cultural objects highlighted in the restitution and repatriation debates