Let A be an n×n real Toeplitz matrix satisfying A+A⊤=2Jn, where Jn is the all-ones matrix. If Ar(i,j) denotes the r×r contiguous submatrix of A consisting of rows i,i+1,…,i+r−1 and columns j,j+1,…,j+r−1, then for every n≥2 one hasdetAn−1(1,2)+detAn−1(2,1)=2detAn−1(1,1). This confirms a conjecture of Charles R. Johnson (2003). The proof combines a rank-one determinant expansion with Dodgson's condensation formula, and then invokes a polynomial-identity argument in the Toeplitz parameters: after obtaining an equality of squares in the integral domain Z[b1,…,bn−1], we factor it to deduce an identity up to sign and determine the sign by a suitable specialization. We also give an extension of the Bayat–Teimoori arithmetic–geometric mean identity: for every real accretive matrix A, one has the sharp inequalitydetAn−1(1,1)detAn−1(2,2)≥|detAn−1(1,2)+detAn−1(2,1)2|, with equality whenever the symmetric part has at most rank one, i.e. A+A⊤=αww⊤ for some α∈R and w∈Rn∖{0}, recovering the Bayat–Teimoori equality as a special case.
Background: Iranian herbal medicines have significant export potential to the Russian market, yet face structural barriers including information asymmetry, lack of digital trust, and regulatory complexities.Aims: This study evaluates the role of electronic platforms in overcoming these challenges.Methodology: Using a mixed-methods approach, data were collected from 36 stakeholders via a structured questionnaire and from 14 experts through in-depth interviews.Findings: Statistical analysis using SPSS revealed that while Russian market demand is high (mean= 4.1/5), traditional export processes remain inefficient due to legal barriers (mean= 2.9/5) and weak after‑sales services (mean= 2.44/5). The correlation between platform adoption and export success is strong and positive (r= 0.72, P< 0.001), while legal barriers have a significant negative relationship with success (r= -0.45). Digital trust (r= 0.65) and after‑sales support (r= 0.61) are also key predictors. Based on expert estimates, digital platforms can reduce buyer discovery time by ~85%, intermediation costs by ~60%, and customs clearance time by ~70%. Also, findings indicate that in the Iran‑Russia context, alignment of digital standards and document transparency are primary prerequisites for building trust. Contrary to expectations, simple and well‑integrated platforms are more effective than complex technologies like blockchain at the current stage.Conclusion: The study concludes that transitioning from traditional methods to an integrated digital ecosystem is not merely an option but a strategic necessity for sustainable export development.
Background: Artificial intelligence has emerged as a general-purpose technology reshaping economic competitiveness, military capability, public administration, and normative order. Between 2020 and 2026, the intensifying competition between India and China has become a defining feature of this global transformation.Aims: This article argues that the India-China AI rivalry transcends mere technical metrics, such as research output or compute capacity, to represent a clash between contrasting models of AI statecraft.Methodology: Drawing on techno-nationalism, neo-realism, and policy-diffusion theory, this study demonstrates that while both nations treat AI as a strategic asset, they organize its development through fundamentally distinct institutional architectures and normative commitments.Findings: China’s approach is characterized by centralized coordination, long-horizon industrial policy, civil-military fusion, and the systematic construction of a sovereign AI ecosystem spanning data, standards, and deployment. Conversely, India’s model, articulated through frameworks like #AIForAll and the IndiaAI Mission, prioritizes inclusive innovation, ethical accountability, digital public infrastructure, and developmental applications. China’s quantitative leadership in scale and infrastructure is tempered by concerns regarding international trust and regulatory legitimacy. Meanwhile, India’s strengths in human capital and ethical framing remain constrained by fragmentation and commercialization gaps. The rivalry carries implications far beyond bilateral relations: it shapes the menu of governance models available to the Global South and influences the evolution of global AI norms, standards, and technological autonomy.Conclusion: By situating this competition within a comparative institutional analysis, the article contributes to scholarship on emerging-technology geopolitics, sovereign AI, and the politics of digital infrastructure in the Indo-Pacific.
در این پژوهش اوجگیری دوبارۀ بحثهای همگانی پیرامون ادعاهای ارضی ایران بر جزایر تنببزرگ، تنبکوچک و ابوموسی در خلیجفارس مطالعه شده است. این خیزش گفتمانی در پی بیانیۀ مشترک اتحادیۀ اروپا و شورای همکاری خلیجفارس در اکتبر ۲۰۲۴م پدید آمد. در این بررسی، ۳۱۲۷ فرستة (پست) یگانۀ فارسیزبان از شبکة اجتماعی ایکس تحلیل شد تا نگرش عمومی و روندهای مضمونی در واکنش کاربران پارسیزبان شناسایی شود. ترکیبی از ابزارهای پردازش زبان طبیعی، ازجمله تحلیل نگرش و روشهای خوشهبندی، برای آشکارکردن الگوهای عاطفی و مضمونیِ دقیقتر بهکار گرفته شد. یافتهها نشان میدهد که توزیع نگرشها متعادل بوده و هشت خوشۀ مضمونی متمایز پدید آمده است که مباحثی چون ادعاهای تاریخی، نقد مداخلههای بیگانگان و تنشهای ژئوپلیتیکی را برجسته میکند. نمودارهای نوآورانه، همچون ابرواژههای مبتنیبر نگرش و نقشههای حساسیت، پیچیدگی واکنشهای عمومی را آشکار میسازد. این تحلیل نشان میدهد که روایتهای درهمتنیدۀ حاکمیت، هویت و ژئوپلیتیک در شکلدهی به افکار عمومی ایرانی نقش بنیادینی دارد و بر نیروهای سیاسیای که در پی جهتدهی به برداشتهای جهانی از مسئلۀ جزایر سهگانه هستند، تأثیری ژرف خواهد داشت.
Growing demand for sustainable lubrication has stimulated the development of bio-lubricants from renewable feedstocks. In this study, canola-oil trimethylolpropane esters (COTMPE) were synthesized by reverse-addition transesterification under vacuum. A Box–Behnken response surface design evaluated the effects of canola-oil methyl ester (COME)-to-TMP molar ratio, catalyst loading, and reaction time on yield. The quadratic model adequately fitted the experimental data and identified reaction time as the dominant variable. Optimal conditions were a COME-to-TMP molar ratio of 4:1, K2CO3 loading of 1 wt%, reaction time of 5.5 h, and 130 °C, giving an overall desirability of 0.90. The model predicted an 86% yield, while independent validation produced 87.5%. Time-resolved GC–FID measurements of TMP monoesters, diesters, and triesters were used to evaluate a mechanistic kinetic–foam model incorporating consecutive acylation, reverse methanolysis, ester scrambling, catalyst deactivation, methanol partitioning, and vacuum sweeping. Methanol removal followed a sigmoidal profile, while the foam fraction peaked near 0.30 during rapid methanol generation. The model reproduced the experimental ester distribution, foam dynamics, and methanol-removal behavior, showing that foam temporarily retained methanol and delayed its removal. Triester formation reached a high fraction of its final value early, followed by diminishing returns at longer reaction times. The resulting COTMPE exhibited a viscosity index of 182, pour point of −9 °C, flash point of 304 °C, and an oxidation induction period of 40 h with 1 wt% propyl gallate. This integrated RSM–kinetic–foam framework provides mechanistic insight into reaction–separation behavior during TMP-ester synthesis.
