This study explores the geometry of timelike ruled surfaces and their associated Blaschke frames in Minkowski 3-space. It establishes a
mapping from spacelike differentiable curves to timelike ruled surfaces and derives the corresponding differential equations governing the
Blaschke frame, which encapsulates key geometric vectors of the surface. Central concepts, such as the striction curve and the Disteli-axis,
are analyzed, highlighting their roles in the surface’s motion and curvature. The research further investigates the conditions for rotational
and translational motions and classifies ruled surfaces based on specific curvature and torsion constraints. Overall, this study offers a
comprehensive framework for understanding the geometry and kinematics of timelike ruled surfaces.

This study investigates the geometric properties of slant timelike-ruled surfaces and their Bertrand offsets in Minkowski space. By deriving
their parametric equations, we examine the structural characteristics of these surfaces and classify their offset relationships. Through the use
of geodesic curvatures, we establish conditions for parallel Bertrand offsets and analyze their compatibility with the Blaschke frame. Explicit
representations of the slant timelike-ruled surface and its Bertrand offset are formulated, with specific parameter values chosen to explore their
geometric behavior. The influence of these parameters on surface geometry is demonstrated through graphical models. These results advance
the understanding of ruled surface theory in Lorentzian geometry and offer valuable insights into applications in mathematical physics and
differential geometry.

In thisstudy,weintroducetheconceptofstationary-angletimelike-ruledsurfacesandexaminetheirgeometricproperties,
particularly inrelationtotheirBertrandoffsets.Atimelike-ruledsurfaceisgeneratedbythemotionofastraightrulingalonga
striction curve,anditsstructureisanalyzedusingtheBlaschkeandDarbouxframes.Wederivekeygeometricinvariants,including
spherical curvature,geodesiccurvature,normalcurvature,andgeodesictorsion.Additionally,weestablishtheconditionsunder
which thestrictioncurveofatimelike-ruledsurfacebehavesasageodesic,anasymptoticcurve,oracurvatureline.Specialcases,
such astimelike-tangentialdevelopablesandtimelike-cones,arealsodiscussed.Usingcurvature-axisanalysis,wedevelopahigher-
order contactframeworktobetterunderstandthebehaviorofthesesurfaces.Finally,weinvestigatetheBertrandoffsetsof
stationary-angle timelike-ruledsurfaces,provingthattheypreserveastationaryanglebetweentheirrulingsanddetermining
the necessaryconditionsfortheirexistence.ThisworkenhancestheunderstandingofdifferentialgeometryinLorentzianspaces
and providesnewinsightsintoruledsurfacesinMinkowskispace.

This study investigates fixed-axis spacelike ruled surfaces and their evolute offset counterparts
within E31
(Minkowski 3-space). The analysis utilizes the Blaschke frame associated
with the striction curves of these surfaces. Spacelike ruled surfaces play a crucial
role in various fields of both classical and modern physics. The research begins by introducing
the fundamental concepts of fixed-axis spacelike ruled surfaces and defining a
height function that establishes the necessary criteria for a ruled surface to be classified
as a fixed-axis spacelike ruled surface. Subsequently, the study derives parameterization
for both the fixed-axis spacelike ruled surfaces and their evolute offsets. Finally, several
surface models are extended and visually represented through graphical illustrations.

In this paper, we propose a method for constructing families of spacelike
surfaces in Minkowski 3-space 𝔼31
that share Bertrand curves as asymptotic
curves. By using marching-scale functions, we derive the necessary conditions,
provide flexible formulations, and establish a framework for constructing mutual
spacelike Bertrand curves. Examples show how different functions generate
surfaces interpolating the common asymptotic curves, offering new insights for
geometric modeling and ruled surface theory.

The developable surface (DS) is a curved surface that can be spread out on a plane without stretching or tearing, which is
widely operated in much fields of engineering and industrialization. This research displays a new approach of producing developable
surfaces in E3(Euclidean 3-space). At first, we start a modified frame over a curve, named as the quasi-frame. We then initiate an
exemplification of a DS and call it a quasi-normal DS. At the essence of this work, we examine the existence and uniqueness of such
DS, then consider its categorizations via singularity theory and unfolding theory (UT). Finally, two paradigms related to our approach
are presented for the purpose of clarity.

This study examines the kinematic geometry of line congruences in Euclidean 3-space
E3, defined as two-parameter families of lines determined by a director surface and unit
direction vectors. The fundamental properties of ruled surfaces within a line congruence
are analyzed, with particular focus on their developability conditions and classification
into torsal and non-torsal surfaces. The dual unit sphere representation is introduced,
along with the fundamental forms of line congruences, leading to the derivation of mean
and Gaussian curvature parameters. Additionally, the study explores the relationships
between principal ruled surfaces and their curvature properties within the kinematic
framework. Furthermore, Hamilton and Mannheim formulae are derived, offering deeper
insights into the differential geometry and motion of line congruences.

Background Regarding their distinct physico-chemical and bioactivity characteristics, silver nanoparticles ‘AgNPs’ are
extensively utilized in numerous scientifc purposes.
Results Within this current investigation, for the frst time, we evaluated how the extracellular extract of the
isolate MAK223 generated exceptionally fxed AgNPs. The isolate was genetically identifed as Aspergillus templicola
OR480102. The generated AgNPs’ physico-chemical characteristics were assessed using ultraviolet-vis spectroscopy,
transmission electron microscopy (TEM), and Fourier transform infrared spectrometry (FT-IR). The maximum
absorption in the UV-vis spectrum was obtained at 420 nm, matching the silver nanoparticles’ surface plasmon
absorbance. A. templicola OR480102 produced uniformly dispersed AgNPs between 5 and 25 nm with a mean
dimension of 17.78537 ± 1.36 nm using TEM. FT-IR analysis identifed functional groups (e.g., -OH, C = O) in the
fungal fltrate that mediate AgNP synthesis and capping. To verify AgNPs stability, the dynamic light scattering
(DLS) approach is employed. Optimal conditions for AgNPs synthesis were 10 days of incubation, one mM silver
nitrate concentration, pH 11, and elevated temperatures. AgNPs demonstrated efcacy against clinically relevant
pathogens: S. typhimurium ‘ATCC 14028’, B. subtilis ‘ATCC 6633’, S. aureus ‘ATCC 25923’, and E. coli ‘ATCC 29213’ were
used in the study. Also, using AgNPs derived from the fltrate of A. templicola OR480102 shows signifcant potential
as a novel therapeutic approach against breast cancer cells ‘MCF-7’. The scratch assay of ‘MCF-7’ cells demonstrates
the suppressive impact of AgNPs for these cell lines during proliferation by promoting apoptosis and reducing cell
migration.
Conclusion Based on physico-chemical characteristics of AgNPs’ and their antimicrobial and anticancer activities,
it cleared that the selected strain Aspergillus templicola OR480102 is a promising producer of stable AgNPs’ with
signifcant bioactivities which could be applicable in different felds. 
 

Geothermal resources in Egypt are useful as a promising source of renewable energy. Little attempts have been carried out to expansively investigate the geothermal potentiality in the Western Desert. The present study is focused on the investigation of geothermal resources in the Northern Western Desert. To achieve this objective, the available aeromagnetic data is firstly reduced to the pole (RTP), then filtered using tilt derivative (TDR) and Butterworth low and high pass methods. The major trends of the different predominant detected local and regional lineaments (probably basement structures) have been determined and correlated with surface structures. To delineate the basement depth configuration, power spectral analysis of aeromagnetic data, as well as constructing 2D modeling (verified by drilled wells data) were applied. The results have been used to estimate the Curie point depth (CPD), geothermal 

The Precambrian Homrit–Waggat granite is a post‐orogenic batholithic intrusion located in the northern region of the Nubian Shield, characterized by a typical annular morphology and significant secondary alteration. This study aims to elucidate the processes that have shaped the intrusion in both macroscopic and microscopic perspectives, employing a combination of field observation and petrographic analysis alongside major and trace element compositions of minerals. Within the central region of the pluton, biotite and amphibole are observed sporadically, while the predominant crystallization of anhydrous oligoclase in the outer regions has led to a progressive increase in volatile components within the residual melt, ultimately resulting in a volatile‐saturated aluminosilicate melt. The exsolved fluids subsequently interacted with the previously crystallized mineral assemblage, producing metasomatic