There is vast increment in the domain of Neuro-Symbolic Artificial Intelligence (AI) that produces
systems
capable of recognizing robust patterns and used for higher level reasonings. The main issue these
systems
face includes requirements regarding big datasets and limited processing complexity. So, to overcome
these
limitations we have developed a ground breaking algorithm that uses neural networks, symbolic reasoning
and quantum computing and named it as Neuro-Symbolic Q-Learning (NSQL). We are the first to add
quantum computing techniques in this domain of Neuro-Symbolic Learning to develop NSQL. NSQL
resolves the main limitations regarding safety while enhancing the interpretability and scalability
aspects
which affect Reinforcement Learning (RL) paradigms. NSQL uses quantum circuit for exploration,
quantum neural network for function approximation and quantum logic gates for symbolic reasoning. This
triad enthusiastically operates with high dimensional state-action spaces in particular for scenarios
with low
probability but have high impact on outcomes. Actually, we have tested our NSQL algorithm with standard
RL problems such as Cart Pole, Mountain Car and Lunar Lander and on various datasets like autonomous
driving data, healthcare diagnostics, financial forecasting to name a few collected from various
sources,
and through online simulating software proved the efficiency of our NSQL algorithm that outperforms all
the available existing advanced algorithms in this domain invented till date. We have given the tabular
results we observed through simulating software and provided the graph we observed and concluded. Our
NSQL shows superior safety, better efficiency and accuracy while maintain interpretability of neural
networks. NSQL shows a big leap in the domain of Reinforcement Learning and shows the potential of
quantum computing in AI guiding way for intelligent systems capable of human like reasoning and
learning.
This research act as bridge between human and artificial cognition.
keywords: Neuro-Symbolic Quantum Learning, Quantum Logic Circuit, Quantum Neural
Network,
Reinforcement Learning, Symbolic Reasoning, High Dimensional State Spaces.
Despite the advancement in fluid dynamics and industrial working fluids, the absence of Jeffrey
parameter
(as in Newtonian fluid) limits these fluids’ ability to represent complex viscoelastic fluids, which are
ideal
for chemical analysis, DNA solutions, and bio-polymer industries. Therefore, this work attempts to
present
the significance of Jeffrey fluid on magnetohydrodynamics (MHD) flow in a heated superhydrophobic
microchannel in the presence of viscous dissipation effects. The formulated nonlinear governing
equations
in terms of temperature and velocity gradients are solved using the regular perturbation method.
Illustrative
graphs are plotted to demonstrate the influence of key parameters embedded in the flow formation, and
the
obtained results are discussed. It is revealed that the action of increasing the Jeffrey fluid parameter
is to
slow down the fluid velocity, due to its viscoelastic properties. The accuracy and correctness of the
present
analysis is established as it is compared with previous works for limiting cases. It is concluded that
this
model will provide a realistic and better approximation to most physiological fluids which are crucial
for
modelling blood flows, polymer solutions, and peristaltic flows of non-Newtonian form. keywords: Natural convection, Magnetohydrodynamics (MHD), Jeffrey fluid parameter,
Viscous
dissipation, superhydrophobic surface, Slit Microchannel.
This paper presents a semi-empirical framework for analyzing and predicting internal friction in porous
metallic materials, with application to foamed aluminum. The formulation integrates acoustic-wave
scattering concepts with continuum theories of elastic materials containing voids to derive closed-form
expressions for the complex wave number, effective elastic moduli, and mechanical loss factor as
functions of porosity, pore geometry, excitation frequency, and strain amplitude. Four physically distinct
dissipation mechanisms are incorporated: void-relaxation damping with empirically identified material
parameters, thermoelastic damping based on classical relaxation theory, amplitude-dependent interfacial
friction calibrated from experimental observations, and acoustic radiation estimated through order-ofmagnitude
analysis. The resulting composite damping relation is formulated using a weak-coupling
perturbation approach rather than exact linear superposition. The model was calibrated and validated
against multiple independent experimental datasets, demonstrating accurate prediction of internal friction
over a broad range of frequencies, porosities, and strain amplitudes within experimental uncertainty limits.
Sensitivity analysis identified the void–elastic coupling modulus β as the primary source of predictive
uncertainty. The results show that damping increases monotonically with porosity in the investigated
range (C = 0.50–0.90), while optimized gradient-porosity architectures can further improve damping
performance at constant mass, providing useful design guidelines for lightweight porous metallic
materials.
keywords: internal friction, metal foams, porous materials, Cowin–Nunziato theory, Lewandowski
model, wave-based modelling, damping, acoustic attenuation, gradient porosity, uncertainty
quantification
In oscillating flow problems, ignoring nonlinear density variation can lead to an inaccurate estimation of
velocity amplitude. Therefore, this paper examines the significance of nonlinear density variation with the
Jeffrey parameter on time-dependent MHD oscillatory flow along a permeable plate. The exact solutions
to the dimensionless equations have been obtained. Given the predicted oscillatory pressure gradient, the
resulting linear partial differential equations were simplified to a boundary-valued problem in which
unsteady flow is superimposed on mean steady flow. The effect of embedded parameters dictating the flow
behavior is demonstrated graphically and explained thoroughly in line with fluid dynamics and engineering
applications. The presence of a nonlinear density parameter is observed to significantly enhance the fluid
velocity, while the Jeffrey parameter acts to bring down the fluid’s speed. It is concluded that the findings
from this research will improve heat transfer and flow stability analysis in convection-driven systems,
leading to a more accurate and comprehensive model.
keywords: Unsteady flow, Nonlinear Variable, Jeffrey parameter, magnetized oscillatory flow,
asymmetric wall heating.
The traditional Affine Cipher is simple to use but easy to break. Its main weakness is that it replaces
each letter with the same ciphertext letter every time. This allows attackers to use letter frequency
analysis to crack the code. This paper presents a modified version called the Segmented Affine
Cipher. The new design splits the message into small blocks. Instead of using one key for the whole
message, it creates a new key for each block. The key for each block depends on the previous
block's ciphertext. This means the same plaintext letter encrypts to different ciphertext letters in
different parts of the message. As a result, the final ciphertext contains all letters at roughly the
same frequency. Attackers cannot rely on matching common letters like "E" to crack the code. The
encryption and decryption steps remain simple, using only basic math that authorized users can
perform easily. The only extra requirement is agreeing on a starting value and block size
beforehand. While a single transmission error can affect multiple blocks, this trade-off is
acceptable for the gain in security. Overall, the Segmented Affine Cipher offers a practical balance
between ease of use and stronger protection against frequency analysis.
Cryptography has undergone significant transformation from simple classical techniques to highly
sophisticated modern encryption systems. Among the earliest known methods, the Caesar Cipher
stands out for its simplicity and historical importance. However, despite its educational value, it
suffers from serious cryptographic weaknesses, particularly its vulnerability to frequency analysis
and brute-force attacks due to its monoalphabetic structure and small key space. This study
introduces a novel modification termed the Position-Dependent Dynamic Caesar Cipher. The
proposed system enhances the classical Caesar Cipher by integrating three major improvements:
an extended character domain, dynamic key scheduling, and position-dependent shifting. These
features collectively transform the cipher into a polyalphabetic encryption scheme, thereby
significantly reducing the statistical predictability of ciphertext. The methodology is grounded in
modular arithmetic and algorithmic design, ensuring that both encryption and decryption processes
remain simple and efficient for legitimate users. The system is evaluated through theoretical
analysis and practical demonstrations, focusing on resistance to frequency analysis, key space
expansion, and computational feasibility. The results show that the proposed cipher effectively
eliminates fixed substitution patterns and introduces sufficient complexity to resist classical
cryptanalytic attacks. While not intended to replace modern cryptographic standards, the Position-
Dependent Dynamic Caesar Cipher provides a meaningful bridge between classical and
contemporary cryptography, making it suitable for educational purposes, lightweight systems, and
constrained environments.
keywords: cryptography, Caesar Cipher, polyalphabetic, cryptanalysis, security analysis.
The current research investigates the effect of mixed-convection flow with Soret wall-concentration effects
on a chemically reactive fluid in a superhydrophobic microchannel containing porous materials. One of the
parallel plates has been deliberately constructed with an extremely hydrophobic surface, while the other
has a non-slip surface. We employ a semi-analytical technique (regular perturbation) to address the highly
nonlinear ordinary differential equations governing mass diffusion, temperature, and momentum.
Illustrative plots were created to show the behavior of major parameters contained in the flow settings. The
results of this study show that an increase in the mixed convection parameter enhances hydromagnetic flow
in the microchannel, resulting in higher shear stress at the channel walls. On the other hand, the presence
of thermo-diffusion value optimizes flow behavior in the microchannel. Key applications of these findings
can be found in pharmaceutical and fine chemical synthesis, where many reactions are highly exothermic.
Certain biochemical assays, like PCR (Polymerase Chain Reaction), involve thermal cycling and
exothermic binding. Additionally, the interaction between mixed convection and the Soret effect allows
for the precise "sorting" of DNA or proteins based on their thermal diffusion coefficients.
keywords: Mixed convection, Thermal diffusion, Arrhenius kinetics, symmetric wall concentration, porous
Microchannel.
In this paper, we present a solution for a class of Neutrosophic Partial Differential Equations (NPDEs)
using the concept of One-Dimensional Geometric AH-Isometry. The main objective of this study is to establish a
clear mathematical framework for defining Neutrosophic Partial Differential Equations and to investigate their
fundamental properties. In this context, we address the Neutrosophic Heat Diffusion Problem, where the obtained
results provide a rigorous methodology for understanding the mathematical and physical characteristics of this
problem and open new perspectives for its practical applications in related fields of mathematical modeling.
keywords: One-Dimensional Geometric AH-Isometry; Neutrosophic Partial Differential Equation, Heat
Diffusion Problem, Adomian Decomposition method.
Topographic altimetric networks constitute a fundamental component of infrastructure development,
providing reliable height references for engineering works and hydrological analysis. The maintenance and
periodic updating of these networks are essential to ensure their long-term consistency and accuracy.
Traditionally, network adjustment is performed using the Weighted Least Squares (WLS) method, which
provides benchmark estimates together with their associated uncertainties. However, incorporating new
observations generally requires reprocessing the complete set of original measurements, which may not
always be available. To address this limitation, the Sequential Weighted Least Squares (SWLS) approach
was applied to a vertical control network located at the Engineering Faculty of the National University of
La Plata. This method allows the network to be updated using only the results of the previous adjustment
(namely the estimated parameters and their covariance matrix) together with the newly incorporated
observations, without requiring access to the full original dataset. The updated benchmark values and their
uncertainties were successfully obtained through the sequential procedure. Additionally, statistical tests
were implemented to evaluate the consistency of the updated network. The Chi-square test was used to
assess the global adjustment quality, while the Chow test was applied to detect potential structural changes
between the original and updated networks. Results indicate that the Chow statistic was not sufficiently sensitive to detect the structural modification introduced in the updated network, whereas the chi-square
test proved more effective in identifying inconsistencies. The proposed SWLS algorithm demonstrated
practical applicability for real-time updating of altimetric networks.
keywords: Altimetric Networks, Sequential Weighted Least Squares, Network Adjustment, Structural
Change Test.
This paper introduces a novel hybrid numerical framework, referred to as the Galerkin–Nyström–Taylor
(GNT) method, for solving Fredholm integral equations of the second kind within the Hilbert space 𝐿2[𝑎, 𝑏].
The proposed method is applicable to both smooth and weakly singular kernels, addressing a significant
challenge in integral equation theory. The GNT approach integrates three powerful components: a Galerkin
projection based on Legendre polynomials, a Nyström iteration employing Gauss–Legendre quadrature
with 2𝑛 nodes, and a localized Taylor expansion correction of order 𝑚 = 4 or 6 near the diagonal to
effectively regularize weak singularities.
A rigorous theoretical analysis establishes super convergence rates, achieving 𝑂(ℎ2𝑛+2) for smooth kernels
and 𝑂(ℎ𝑛+1+𝑚) for weakly singular kernels. These results significantly exceed the convergence behavior
of classical methods.
Extensive numerical experiments are conducted on six benchmark problems, including smooth, weakly
singular, and physically motivated models, as well as linear and nonlinear Hammerstein-type equations.
The results demonstrate that the proposed GNT method outperforms classical Galerkin and Nyström
methods by 3–4 additional orders of accuracy, while also improving computational efficiency by
approximately 35%.
To the best of our knowledge, this hybrid formulation has not been previously reported in the literature, and
it offers a substantial and original contribution to the numerical analysis of integral equations.
keywords: Fredholm integral equations; projection methods; Galerkin method; Nyström method; Taylor
correction; super convergence; weakly singular kernels; Hilbert spaces.
For photon-induced electron–positron cascades in dense pair media we formulate and assess a compact analytical onset criterion. The construction is counting-consistent in that only local collision probabilities, Klein-Nishina angular acceptance and a mesoscopic connectivity correction allow microscopic event counts to enter. This is the expression for the single-step trigger probability Ptrig = Ploc · Pang · ηeff, where the probability of at least one pertinent local scattering over a representative path length is indicated by Ploc, Pang represents the Klein-Nishina-weighted acceptance connected to a given energy-transfer or recoil gate, and ηeff gathers unresolved suppression effects including radiation reaction, phase-space constraints, crowding degeneracy and model-resolution losses. The connectivity-corrected onset condition is λκc = (ρV3(r)/κc) · Ploc · Pang · ηeff > 1. Density, geometry, microscopic kinematics and graph connectivity are all neatly separated in this form which offers a clear diagnostic for threshold estimation and simulation design.
keywords: electron–positron cascade; dense pair plasma; Klein–Nishina scattering; random geometric
graph; continuum percolation; analytical onset criterion; pair media
In this paper, we develop a solution framework for a class of Neutrosophic Partial Differential Equations
(NPDEs) based on the concept of Refined AH-Isometry. The primary aim of this study is to establish a
rigorous and coherent mathematical formulation for NPDEs, along with a systematic investigation of their
fundamental structural and analytical properties. In addition, the proposed approach highlights the
effectiveness of Refined AH-Isometry in handling the indeterminacy inherent in neutrosophic
environments, thereby providing a flexible and reliable tool for solving such equations.
keywords: Refined AH-Isometry; Neutrosophic Partial Differential Equations.
We will look at two problems where the unknown source must be found.
We consider the problem of finding a pair of functions a(𝑥) and 𝑤(𝑥, 𝑡) that satisfy the equation
𝑤𝑥𝑥(𝑥, 𝑡) + 𝑤𝑡𝑡(𝑥, 𝑡) = 𝑎(𝑥)𝑤(𝑥, 𝑡) under Cauchy boundary conditions.
And also we consider the problem of finding a pair of functions 𝑟(𝑡) and 𝑤(𝑥, 𝑡) that satisfy the equation
𝑤𝑡(𝑥, 𝑡) = 𝑤𝑥𝑥(𝑥, 𝑡) + 𝑟(𝑡) under Cauchy boundary conditions.
We will see that an approximate solution can be found using the techniques of generalized inverse problem
of moments and find dimensions for the error of the estimated solution.
keywords: generalized moment problem; integral equations; Elliptic equation, Parabolic
equation, inverse source.
Here ,we investigate the three-point integral boundary value problem for functional
differential equation
𝑢″ + 𝑎(𝑡)𝑝(𝑢,𝑢′) + 𝑏(𝑡)𝑞(𝑢,𝑢′) = 0, 𝑡 ∈ (0, 1),
𝑢(0) = 0, 𝛼∫0𝜂𝑢(𝑠)𝑑𝑠 = 𝛽∫0𝜂𝑢(𝑠)𝑑𝑠 = 𝑢(1), where 0 < 𝜂 < 1 and 0 < 𝛼, 𝛽 < 2 / 𝜂2.
And proved the existence of at least one positive solution through the fixed point theorem.
keywords: Functional differential equation, Fixed point, integral boundary value problem.
In a vertical cylindrical tube, an unsteady analysis of a nonlinear mixed convection flow driven by Brownian
motion and the thermophoresis parameter is accomplished using nanoparticles. The governing equations
for momentum, temperature, and nanoparticle volume fraction are calculated. The closed-form solutions
for the flow configuration are derived through direct integration and parameter variation. Due to the
unsteady state component's highly nonlinear nature, an implicit finite difference method is employed to
derive the numerical solution after discretizing the flow equations. The impact of critical parameters on
momentum, energy, mass diffusion, and nanoparticles, including skin friction and heat/mass transfer rates,
is given and explained in detail using illustrated graphs. To verify the correctness and validity of the current
analysis, a numerical comparison is performed between the analytical and numerical solutions for the
classic example at large times; good consistency was observed. The use of a mixed convection parameter
in a vertical tube nanofluid flow dramatically improves heat transmission by combining buoyancy forces
with forced convection, resulting in a more stable and enhanced fluid flow. Furthermore, it is discovered
that the existence of a nonlinear variable increases the velocity of fluid flow, which is caused by axial
buoyancy forces, confinement, and particle movement, which are closely related in this geometry. The
findings of this work have applications in high-performance computing, microelectronic packaging, and
vehicle demisters/defrosters, where nanofluids act as superior coolants.
keywords: Unsteady flow, Mixed convection, Nonlinear variable, Nanofluid, Brownian motion,
thermophoresis, vertical cylindrical tube.
This work studies fully developed free convection flow in a temperature-dependent variable
viscosity over an upright porous microchannel with velocity slip and temperature jump conditions.
The Arrhenius-controlled heat transfer flow is investigated for various wall-ambient temperature
difference ratio scenarios. The extremely nonlinear governing equations are semi-analytically
solved with the homotopy perturbation technique (HPM). The Reynold model represents
temperature-dependent viscosity using an exponential function. The primary goal of the study is
to describe the effects of altering viscosity and Darcy porous media in a chemically reactive fluid.
The discovered solutions are visually illustrated and thoroughly described. As the temperature
builds because of the exothermic process, the buoyant force typically overpowers the Darcy
resistance. This causes an increase in fluid velocity, particularly if the medium is highly permeable.
The interconnecting ligaments (pores) greatly increase the fluid-solid contact area compared to a
simple microchannel. Furthermore, it is revealed that a higher viscosity variation parameter
increases both fluid velocity and shear stress on the lower plate. The findings of this work will
have implications for biological and chemical engineering applications such as catalytic packedbed
reactors, bioreactors, and waste treatment. In many applications, the porous structure serves
as both a flow regulator and a thermal stabilizer. Researchers can utilize the findings of this work
for bio-microfluidic systems and heat management in microelectronics, where properties change
rapidly with temperature.
keywords: Variable viscosity, Darcy Porous medium, exothermic fluid, wall ambient
temperature difference ratio, Rarefaction parameter, homotopy perturbation method (HPM).
This article explores the significance of heat and mass transfer affected by a concentration jump in a
buoyancy-induced magnetized flow with viscous dissipative fluid across a superhydrophobic (SHO)
microchannel. While the other parallel plate has a no-slip surface (NSS), one of the plates is purposefully
altered to create a superhydrophobic surface (SHS). The nonlinear coupled ordinary differential equations
are solved semi-analytically. A graphical representation shows how the main parameters govern the flow
behaviour in terms of momentum, temperature, and concentration distributions. It is concluded that the
action of the buoyancy term is to accelerate or decelerate the fluid velocity depending on whether N > 0 or
N < 0. On the other hand, a higher concentration jump parameter is seen to decrease the mass diffusion
effect in the microchannel. A concentration jump represents the effective driving force in a mass transfer
coefficient. Therefore, this research can find applications in gas-liquid absorption, liquid-liquid extraction,
solid-fluid transfer, membrane processes, and biological systems.
keywords: Mass Transfer, Viscous Dissipation, Sustentation parameter, Temperature jump,
Concentration jump, Superhydrophobic Microchannel.
