Advances in Applied Mathematics and Computing
Advances in Applied Mathematics and Computing (AAMC) is an international peer-reviewed, open-access journal that publishes high-quality research in applied mathematics, computational science, and advanced computing. The journal covers mathematical modeling, numerical analysis, optimization, scientific computing, computational intelligence, data analytics, machine learning, simulation techniques, and interdisciplinary computational applications. It provides a platform for innovative research that advances mathematical methods and computational technologies for solving complex real-world problems.
DIGITAL TRANSFORMATION AND ORGANIZATIONAL PERFORMANCE: THE MEDIATING ROLE OF ORGANIZATIONAL AGILITY AND MODERATING EFFECT OF ENVIRONMENTAL TURBULENCE
Digital transformation has become a strategic imperative for organizations seeking to improve performance and sustain competitiveness amid increasingly turbulent business environments. This study examines the effect of digital transformation on organisational performance, focusing on the mediating role of organisational agility and the moderating effect of environmental turbulence. A sequential explanatory mixed-methods design was adopted, combining a quantitative survey with qualitative interviews. Quantitative data were obtained from 452 valid responses across 65 medium-sized and large organizations in information technology, financial services, manufacturing, telecommunications, and healthcare. Data were analyzed using descriptive statistics, measurement-model assessment, reliability and validity testing, Structural Equation Modelling (SEM), mediation analysis, and moderation analysis. Qualitative data were obtained through semi-structured interviews with 25 purposively selected participants and analyzed thematically. The results show that digital transformation significantly enhances organisational agility (β = 0.686, p < 0.001; R² = 0.47), while organisational agility significantly improves organisational performance (β = 0.553, p < 0.001). Organisational agility significantly mediates the relationship between digital transformation and organisational performance (indirect effect = 0.380, p < 0.001), while environmental turbulence significantly moderates the relationship between digital transformation and organisational agility (β = 0.217, p = 0.001). The study contributes an integrated framework demonstrating how organisational agility serves as a mechanism through which digital transformation generates performance benefits and how environmental conditions shape this relationship.
Copyright (c) 2026 Atinuola Elizabeth Ayeoribe, Olarewaju Peter Ayeoribe (Author) https://creativecommons.org/licenses/by/4.0
MATHEMATICAL CORRELATION OF IC50 AND MIC OF HYDROPHOBIC ANTIBIOTICS FOLLOWING COMPETITIVE INHIBITION IN THE DISK DIFFUSION METHOD
Objective: This study explores the mathematical link between binding affinity, drug resistance, IC50, MIC, and Zone of Inhibition (ZOI) in the disc diffusion method for antimicrobial susceptibility testing. We consider ZOI (x) as a response to antibiotic concentration, showing that x is proportional to –log (MIC) and correlated with the binding free energy (exp ΔG). Our findings establish a clear relationship between binding affinity, MIC, ZOI, and antibiotic concentration (c) for hydrophobic antibiotics under competitive inhibition in the disk diffusion method, the value of half Maximal inhibitory concentration IC50 is equal to the twice of minimum inhibitory concentration to the multiple of exponent of fraction of Zone of Inhibition ‘x’ and dissipative term “V” by twice the diffusion term. It will Contributing to a better understanding of resistance mechanisms. Methods: The mathematical derivations are been validated by the published data available from the journal such as MIC, diffusion constant (D), ZOI (x) and IC50 values and Dissipative Value (V) has been calculated and calculated, IC50 values are compared with reported values. Result: The data had been validated for ∆G, Dissipative Value (V), IC50 values from predictive to reported it had been observed that while calculating IC50 values of resistance and non-resistance susceptibility, the MIC value for resistance group is more hence the value of IC50 will depreciates and depend more on values of ZOI (x) and V the dissipative term Table 1 revels while analysing the ratio between resistance and non-resistance MIC and IC50 shows direct relationship it can be cross verified by reported and calculated values, Levofloxacin IC50 values ranges from 9.81- 3.2 µg/ml while calculated value is 10-1.6 µg/ml, binding energy ∆G reported is -6.57 and calculated is -7.72 to 7.82 K Cal/mol (Table 1) similarly with ciprofloxacin the value of IC50 for non-resistant to resistant is 3.5- 10 µg/ml where Mic is 0.001-0.5 µg/ml, binding energy reported -7.13 and calculated was 8.37 Kcal/mol. In the case of Tetracycline, the value of reported IC50 was 35- 47 µg/ml and calculated is 54-60 µg/ml and value of reported and calculated ∆G is -12.48 and -7.62 to 7.07K Cal/mol respectively. The reason behind difference of ∆G is, large value of V 4.16 and 2.23 for tetracycline. Significance: The equations and derivation give better understanding between ZOI (x) and Dissipative Value (V) we can predict the resistance and factors effecting resistance which give low value of ZOI (x) against same concentration of antibiotics against non-resistance bacteria
Copyright (c) 2026 Viqar Agha, Mohammad Asif (Author) https://creativecommons.org/licenses/by/4.0
CODING/DECODING NUMBER ARRAYS COUNTING IN TRIPLETS
Following research of the same author on 'Logical Principles in Ternary Mathematics,' we would like to improve the model that was proposed in the aforementioned article by the diagram that links decimal numbers, number arrays, and triplets. The latter has to undergo some specification. Here the term 'trits' implies not only a set of three numbers as in ( ) It is also a three-component vector It's a very important provision because it links a vector space, an integer, and a number array; each of them being an independent unit.[6] Understanding concepts like 'vector space,' 'integer,' and 'triplet' can be challenging, especially for someone new to the topic. It's easy to feel confused by the terminology used. So, let's move on swiftly and illustrate this idea with an example: This principle will define our analysis given below.
Copyright (c) 2026 Ruslan Pozinkevych (Author) https://creativecommons.org/licenses/by/4.0
SPECTRAL TOPOLOGY OF GLOBAL IMBALANCES: A GRAPH-THEORETIC FRAMEWORK FOR SYSTEMIC RISK IN THE BALANCE OF PAYMENTS
We model global balance-of-payments linkages as a directed weighted exposure network and study systemic fragility through the spectrum of the associated operators. From a signed bilateral-flow matrix we construct a nonnegative exposure lift, derive a spectral stability criterion for linear propagation, and define node- and edge-level risk measures using Perron–Frobenius geometry, PageRank, and marginal spectral impact. We further give two complementary extensions: a directed Laplacian formulation for shock diffusion and a non-backtracking threshold for cascade formation on sparse exposure networks. The framework identifies systemic risk as a topological property of the global network, rather than a collection of isolated country indicators, and yields mathematically explicit diagnostics for resilience, concentration of stress, and targeted stabilization.
Copyright (c) 2026 Chandrasekhar Gokavarapu, Sanjeev Kumar Chejarla, Balayya Rajana, V. N. S. R. Murthy Duggirala, Srinivasulu Chittaru (Author) https://creativecommons.org/licenses/by/4.0
DEVELOPMENTS OF THE OPTIMIZATION IN TERNARY CALCULUS
The aim of the aforementioned research is to establish relations between integers n ∈ Z and vectors x ∈ R3 A ternary operation on a set S in mathematics is a function ω : S×S×S → S that maps each ordered triple (a,b,c) ∈ S3 to an element ω(a,b,c) ∈ S This describes a particular example of an n-ary operation for n=3,where the domain is the Cartesian product of three copies of S and the codomain is S itself[1]
REDUCING ERROR RATES AND LATENCY IN ASYNCHRONOUS RADIO NETWORKS VIA STRUCTURED INFORMATION FLOW
The evolution of modern wireless communication systems has heightened the demand for efficient and reliable asynchronous radio transmission mechanisms. This study explores how structured information flow impacts the intricacy, reliability, and overall performance of such systems, particularly under dynamic network conditions. Asynchronous systems, unlike their synchronous counterparts, operate without a global clock reference, resulting in potential timing discrepancies, packet collisions, and signal distortion. By implementing a structured information flow protocol, where data packets follow optimized routing sequences with prioritized buffering and scheduling strategies, the system demonstrates measurable improvements in operational stability and throughput. Simulation experiments conducted on a 5G-inspired wireless testbed revealed that structured information flow reduced packet loss rates from 7.8% to 2.3% and improved end-to-end latency by approximately 18%, compared to unstructured transmission. Additionally, system intricacy, quantified through the complexity metric of protocol state transitions, decreased by 12%, indicating simplified network management without compromising performance. Reliability analysis, performed via bit-error rate (BER) evaluation under varying signal-to-noise ratios (SNRs), showed a reduction from 10⁻³ to 3.5×10⁻⁴ in the structured system, confirming enhanced robustness against channel impairments. The findings suggest that structured information flow not only mitigates intrinsic asynchronous system challenges but also enhances adaptability in multi-node wireless environments characterized by interference and unpredictable traffic patterns. These results are particularly relevant for emerging applications such as Internet of Things (IoT) networks, autonomous vehicular communication, and next-generation mobile broadband, where latency, reliability, and efficiency are critical. This study contributes to the theoretical and practical understanding of asynchronous radio systems and provides actionable insights for designing communication protocols that balance complexity, reliability, and performance in high-demand wireless networks.
Copyright (c) 2025 Advances in Applied Mathematics and Computing https://creativecommons.org/licenses/by/4.0
DEVELOPMENT AND EXPERIMENTAL VALIDATION OF A 315–335 MHZ RF POWER AMPLIFIER FOR SPECIALIZED SHORT-RANGE COMMUNICATION SYSTEMS
This study presents the design, optimization, and practical implementation of a proposed RF power amplifier (RFPA) specifically engineered for operation within nonstandard frequency bands, where conventional amplifier topologies often exhibit reduced efficiency, instability, and significant output power degradation. The amplifier was developed using a Class-AB configuration to balance linearity and efficiency, with a target operational range of 315–335 MHz, a band commonly used for specialized communication systems such as industrial control, short-range telemetry, and customized RF modules. Computer-aided simulations were conducted using ADS and CST Studio Suite to analyze key parameters including gain, power-added efficiency (PAE), output power, harmonic suppression, and stability factor (K). Simulation results showed a peak gain of 18.7 dB, an output power of 27.5 dBm, and a PAE of 54.2% at 325 MHz. The stability analysis indicated a Rollett stability factor K = 1.42, confirming unconditional stability across the entire operational band. To ensure practical viability, the amplifier was constructed on a FR-4 substrate (εr = 4.3, thickness 1.6 mm), using a matched input–output network optimized for minimal insertion loss and maximum power transfer. Laboratory measurements closely matched simulation outcomes, yielding a measured gain of 17.9 dB, output power of 26.8 dBm, and PAE of 52.6%, demonstrating less than 5% deviation from simulated values. Further evaluation included spectrum analysis, which confirmed harmonic suppression greater than –32 dBc for the second harmonic and –41 dBc for the third harmonic. Thermal performance tests indicated a temperature rise of 14°C at full load, remaining within safe operational limits without requiring active cooling. Overall, the study confirms that the proposed RFPA offers a robust, energy-efficient, and stable solution for nonstandard frequency applications. Its strong agreement between simulation and measurement validates its applicability in customized RF systems requiring high reliability, enhanced signal performance, and cost-effective hardware deployment.
COMPARATIVE ANALYSIS OF DIPOLE, YAGI–UDA, AND HELICAL ANTENNAS IN FM TRANSMISSION SYSTEMS FOR IMPROVED SIGNAL STRENGTH, COVERAGE EFFICIENCY, AND BROADCAST RELIABILITY
The study here compares and evaluates the performance of different antennas such as the dipole, Yagi-Uda, and helical antennas in the context of FM broadcasting. The main goal here is to compare how these antennas perform in terms of signal strength and efficiency. The study carried out experiments in a controlled environment and tested the antennas in an outdoor environment by scanning the FM band from 88 to 108 MHz. The experiments were conducted in a similar environment to compare the performance of these antennas. The parameters taken for the study were gain in dBi, SNR, RSSI, bandwidth efficiency, and radiation pattern stability. The results obtained from the experiments show that the dipole antenna performed at an average gain of 2.1 dBi and an RSSI of -64 dBm at a distance of 1 km. The study also found that the SNR for the dipole was 18.4 dB. The results obtained from the experiments show that the dipole antenna performed well at a distance of 3 km. The performance of the dipole antenna was average. The study also found that the Yagi-Uda antenna performed very well in terms of directional efficiency. The results obtained from the experiments show that the Yagi-Uda antenna performed at an average gain of 9.6 dBi and an RSSI of -47 dBm at a distance of 1 km. The study also found that the SNR for the Yagi-Uda antenna was 27.8 dB. The results obtained from the experiments show that the Yagi-Uda antenna performed very well at a distance of 8.5 km. The study also found that the helical antenna performed at an average gain of 6.2 dBi and an RSSI of -55 dBm at a distance of 1 km. The study also found that the SNR for the helical antenna was 23.1 dB. The results obtained from the experiments show that the helical antenna performed very well at a distance of 6.2 km. The study found that the helical antenna performed better in an environment with buildings and foliage. The study concluded that the choice of the antenna depends upon the requirements. The study concluded that the Yagi-Uda antenna should be used for long-distance and high-gain requirements. The study concluded that the helical antennas should be used for difficult propagation environments. The study concluded that the dipole antennas should be used for economical requirements.
BROADBAND DIPOLE ANTENNA WITH INTEGRATED BALUN FOR ENHANCED WIDEBAND AND STABLE COMMUNICATION PERFORMANCE
Broadband wireless communication systems require antennas with wide impedance bandwidth, stable radiation characteristics, high efficiency, and compact structural integration to support reliable multi-band operation. This paper presents the design, optimization, fabrication, and experimental validation of a broadband dipole antenna incorporating an integrated balun to enhance impedance matching, radiation efficiency, and communication stability. The antenna geometry was developed using full-wave electromagnetic modelling and optimized through parametric analysis before prototype fabrication and experimental characterization using a calibrated vector network analyzer. The fabricated antenna achieved a measured operating frequency range of 1.18 - 4.43 GHz, corresponding to an impedance bandwidth of 3.25 GHz and a fractional bandwidth of 113.8%. A minimum reflection coefficient (S₁₁) of -36.8 dB and a VSWR of 1.11 were obtained, demonstrating excellent impedance matching throughout the operating band. The antenna further achieved a measured peak gain of 7.6 dBi, radiation efficiency of 94.5%, and stable radiation patterns across the entire frequency range. Comparative analysis with a conventional dipole antenna revealed bandwidth, gain, and radiation-efficiency improvements of 264.1%, 83.7%, and 13.7%, respectively. Furthermore, the maximum deviation between simulated and measured results remained below 6%, confirming the validity of the proposed electromagnetic model and fabrication process. The integrated balun effectively suppresses common-mode currents, improves current symmetry, and enhances overall antenna performance, demonstrating the proposed design as a robust solution for broadband and stable wireless communication applications.
Copyright (c) 2026 Olarewaju Peter Ayeoribe (Author) https://creativecommons.org/licenses/by/4.0
ADAPTIVE MODULATION AND CODING TECHNIQUES FOR ENHANCING RELIABILITY, POWER EFFICIENCY, AND SIGNAL ROBUSTNESS IN HIGH-POWER DVB-T2 DIGITAL TELEVISION TRANSMISSION SYSTEMS
Adaptive Modulation and Coding (AMC) has become a critical mechanism in optimizing the performance of Digital Video Broadcasting–Terrestrial, second generation (DVB-T2), particularly for high-power transmission systems operating under the EN 302 755 EU standard. This study evaluates the trade-off between spectral efficiency, bit error rate (BER), and carrier-to-noise ratio (C/N) across various AMC profiles at a transmitter power of 5 kW over a 10 km coverage radius. Simulations were conducted using MATLAB DVB-T2 toolboxes and validated with laboratory measurements on a 1 kW prototype exciter. Results show that QPSK 1/2 achieved robust performance at low C/N (3.8 dB) with BER ≤ 10⁻⁷, but spectral efficiency was limited to 1.0 bit/s/Hz. Conversely, 256-QAM 3/4 provided maximum throughput (6.7 bit/s/Hz) but required a C/N threshold of 21.4 dB to maintain BER ≤ 2 × 10⁻⁶. Intermediate modes such as 16-QAM 1/2 and 64-QAM 2/3 offered balanced performance, delivering 2.2 and 4.5 bit/s/Hz at C/N thresholds of 7.9 dB and 14.6 dB, respectively. Laboratory field trials confirmed that adaptive switching between modulation-coding schemes reduced outage probability by 27% compared to static configurations, while improving average spectral efficiency by 18%. These findings demonstrate that AMC under the EN 302 755 standard significantly enhances system robustness and spectrum utilization in high-power DVB- T2 deployments.
FATHER HUMAN SWARM OPTIMIZATION (FATHERHSO): ISVHAAI AI SOCIETY LETTERS
Very Highly Advanced Artificial Intelligence (VHAAI) is the field used by International Society for VHAAI (ISVHAAI) to deal with problems. Father Human Swarm Optimization (FatherHSO) is the novel algorithm designed in this Letter No. 16 of ISVHAAI Artificial Intelligence Society Letters.
EXCELLENCE MONEY HUMAN SWARM OPTIMIZATION (EMHSO): ISVHAAI AI SOCIETY LETTERS
A new field titled Very Highly Advanced Artificial Intelligence (VHAAI) and a new Society titled International Society for VHAAI (ISVHAAI) have been coined and defined in 2024. ISVHAAI Society improves and applies VHAAI field to address various problems. This is the Letter No. 15 of ISVHAAI Artificial Intelligence Society Letters. In this Letter, a new algorithm titled Excellence Money Human Swarm Optimization (EMHSO) has been designed.
S M NAZMUZ SAKIB AND PYTHAGORAS: SAKIBIAN GEOMETRY VS. PYTHAGOREAN GEOMETRY
This paper presents the first comprehensive comparative study of Pythagorean geometry and Sakibian geometry, two mathematical traditions separated by approximately two and a half millennia but united by a shared commitment to discovering the deepest structural properties of space, form, and mathematical relationship. Pythagorean geometry, originating in the philosophical and mathematical program of Pythagoras of Samos in the sixth century BCE, established the foundational principles of Euclidean spatial reasoning and produced the most famous theorem in the history of mathematics: that the square of the hypotenuse of a right triangle equals the sum of the squares of its other two sides. Sakibian geometry, the body of mathematical work produced by S M Nazmuz Sakib, a Bangladeshi polymath scholar born in 2001, constitutes a twenty-first century expansion, generalization, and philosophical reorientation of the Pythagorean program across multiple mathematical domains simultaneously, including triangle geometry, incircle theory, median-altitude decomposition, spectral geometry, graph-theoretic invariants, information geometry, stochastic geometry, and formal category theory. This paper demonstrates that Sakibian geometry does not merely extend Pythagorean results but enacts a fundamental philosophical reorientation of the Pythagorean approach: where Pythagoras seeks a single universal structural identity confined to right triangles in flat Euclidean space, Sakib pursues a plurality of Pythagoras-like structural identities that generalize across triangle types, metric spaces, information-geometric manifolds, and network structures, replacing the condition of right-angularity with the condition of equilaterality as the canonical geometric optimum and replacing the static, deterministic framework of classical Euclidean geometry with an adaptive, context-sensitive, and probabilistically informed mathematical philosophy. The paper situates this comparison within the broader history of mathematics and philosophy of mathematics, examines the philosophical foundations of both traditions, provides detailed technical comparisons of specific theorems and results, traces the cross-domain implications of Sakibian geometry for public health, environmental science, international law, linguistics, and organizational theory, and concludes with an assessment of the significance of Sakibian geometry for the future of mathematical research in the twenty-first century.
Copyright (c) 2026 Jakia Sultana Jerin, Md Hafizur Rahman Khan, Nafija Alam Omi, Dr. Gaurav Rao, Md. Sulaiman Hazbi, Md. Syful Islam (Author) https://creativecommons.org/licenses/by/4.0
S M NAZMUZ SAKIB AND PYTHAGORAS: FROM PYTHAGOREAN GEOMETRY TO SAKIBIAN GEOMETRY
This thesis positions “Sakibian Geometry”—a body of modern theorems and frameworks introduced by S M Nazmuz Sakib—in dialogue with classical Pythagorean geometry. Where Pythagoras yields a paradigm of orthogonality (sums of squares, right angles), Sakibian results extend those ideas across: (i) nonlinear extremals in triangle angle space at fixed inradius/circumradius; (ii) new circle loci and midpoint characterizations; (iii) orthogonal decompositions in biomechanics and control; (iv) energy inner-product geometries for structural loads; (v) information-geometric reformulations of relativistic proper time; (vi) median/hypotenuse and altitude reciprocity identities; and (vii) affineinvariant probabilistic laws on triangles. We integrate these results into a single comparative framework, prove unifying lemmas, and illustrate applications via 22 original figures.
S M NAZMUZ SAKIB AND PYTHAGORAS: A COMPARATIVE DISCUSSION ON SAKIBIAN GEOMETRY AND THE PYTHAGOREAN GEOMETRY
This thesis positions “Sakibian Geometry”—a body of modern theorems and frameworks introduced by S M Nazmuz Sakib—in dialogue with classical Pythagorean geometry. Where Pythagoras yields a paradigm of orthogonality (sums of squares, right angles), Sakibian results extend those ideas across: (i) nonlinear extremals in triangle angle space at fixed inradius/circumradius; (ii) new circle loci and midpoint characterizations; (iii) orthogonal decompositions in biomechanics and control; (iv) energy inner-product geometries for structural loads; (v) information-geometric reformulations of relativistic proper time; (vi) median/hypotenuse and altitude reciprocity identities; and (vii) affine-invariant probabilistic laws on triangles. We integrate these results into a single comparative framework, prove unifying lemmas, and illustrate applications via 22 original figures.
Copyright (c) 2026 Md Nazmul Hossain, Nafija Alam Omi, Md Hafizur Rahman Khan, Md. Sulaiman Hazbi, Aminul Islam, Sabbir Shikdar, Md Shariful Islam, Ronald C Kessler (Author) https://creativecommons.org/licenses/by/4.0
BEYOND CORRELATION: ENHANCING CURRENCY PORTFOLIOCONSTRUCTION THROUGH KENDALL’S TAU ANDCORRESPONDENCE ANALYSIS
Traditional correlation metrics such as Pearson and Spearman are widely employed in financial portfolio construction, yet they exhibit critical limitations. Pear- son correlation, being linear and sensitive to scale and volatility, often overstates de- pendency during high-variance periods, while Spearman correlation fails to capture non-monotonic relationships. In this paper, I advocate a shift from classical cor- relation analysis to a correspondence-based perspective, employing Kendall’s Tau as a more robust and semantically consistent measure of dependency. I demonstrate, through a portfolio optimization framework, that Kendall correlation yields superior results in terms of return maximization and drawdown minimization, particularly under conditions of structural market changes and nonlinear dependencies. Empirical results on historical asset data reveal that portfolios constructed using Kendall-based correspondence measures exhibit enhanced stability and riskadjusted performance compared to those based on conventional correlations. This work highlights the importance of re-evaluating correlation paradigms in favor of more meaningful statistical dependence structures in financial modeling.
Copyright (c) 2025 Advances in Applied Mathematics and Computing https://creativecommons.org/licenses/by/4.0/deed.en