Journal of Kufa for Mathematics and Computer

It is necessary to study the theoretical bases of an approximation deep convolutional neural networks,

because of its interesting developments in vital domains. The approximation abilities of deep-convolution neural
networks produced by downsampling operators in quasi- Orlicz spaces have been studied, since this space is wider
and more important than other spaces. In this paper, we define quasi-Orlicz norm on spherical spaces. In addition,
modulus of smoothness is also studied in terms of quasi-Orlicz norm. Finally, Function approximation theorems are
studied by using convolution neural networks with ???? fully connected layer so that the error is resulted to be equivalent
to double ????-th order modulus of smoothness

The dependability and effectiveness of a network can be investigated using a variety of graph-theoretic
techniques and the network's connectivity determines how reliable it is. Diameter in a network is often used to
measure the efficiency of a network if a network experiences issues such as a decline in the communication signal or a
breakdown in the communication between its components. This paper examines the increase in diameter of the
generalized Petersen graph ????????(????, ????) after removing a certain number of edges. Finding the exact values of ????(????, ????)
that represents the maximum diameter of an altered generalized Petersen graph ????????(????, ????, ????) obtained after removing ????
edges from ????????(????, ????) for ???? = 1 and ???? ≥ 2.

The explicit form of Harnack’s inequality for non-negative harmonic functions in the open ball ????????̃(????)
plays an important role in harmonic analysis and elliptic partial differential equations. In this paper, we establish the
explicit form of Harnack’s inequality for Poisson’s Dirichlet problem in the open ball ????????̃(????) with non-negative
boundary data. We involve the Green’s function for Laplacian operator to find it out. Harnack’s inequality for
positive harmonic functions can be followed from Harnack’s inequality for Poisson’s Dirichlet problem when the
source function is set to be zero.

Let ???? = (????, ????) be a graph with ???? = ???? (????) and ???? = ????(????). A function ???? ∶ ???? → {0, 1, 2} is
said to be an Italian dominating function on a graph ???? if every vertex ???? with ???? (????) = 0 is adjacent to at
least one vertex ???? with ???? (????) = 2 or is adjacent to at least two vertices ????, ???? with ???? (????) = ???? (????) = 1.
The value ????(???? ) = ∑???? (????) denotes the weight of an Italian dominating function. The minimum ????∈???? weight taken over all Italian dominating functions of ???? is called Italian domination number and denoted
by ????????(????).
Two parameters related to Italian dominating function (IDF) are restrained Italian (RIDF) and total
restrained (TRDF) dominating functions ???? , for which the set of vertices ???? with ???? (????) = 0, and
simultaneously the set of vertices ???? with ???? (????) > 0 and the set of vertices ???? with ???? (????) = 0 induce
subgraphs with no isolated vertex respectively. The central graph ????(????) of a graph ???? is the graph obtained
by subdividing each edge of ???? exactly once and joining all the non-adjacent vertices of ????.
In this work, we initiate the study of restrained (total restrained) Italian domination number of the
central of any graph ????. For a family of standard graphs ????, we obtain the precise value of restrained (total
restrained) Italian domination number for ????(????), indeed for any graph G, the sharp bounds are provided for
????(????), and for ???? corona of ????1 , ???? ∘ ????1 we establish the precise value of these parameters for ????(???? ∘ ????1).

Alzheimer's disease is a severe, neurodegenerative condition that gradually breaks memories, thinking
abilities, and the ability to carry out even the most basic tasks. The hub genes of AD were examined in this study.
They understand how interactions between proteins and non-protein substances are crucial to understanding how
proteins work. Network investigations of protein-protein interactions, in particular, help understand biological issues.
This article offers a novel approach to identifying essential proteins using weighted PPI networks and HyperlinkInduced Topic Search (HITS) algorithm. We discovered thetop 10 hub genes linked to AD using a protein network analysis:

AKT1, TGFB1, GRB2, NFKB1, PIK3CA, PIK3R1, TNF, IFNG, VEGFA, and TP53. It was discovered by
gene enrichment that most gene activities might be categorized as vital to the plasma membrane, including
engagement in signaling cascades, G-protein composite reliability activation, and cell contact. The prioritized genes
were determined by the convergent functional genomics ranking AKT1, TGFB1, GRB2, NFKB1, PIK3CA, PIK3R1,
TNF, IFNG, VEGFA, and TP53. To better understand AD pathophysiology and find new biomarkers or medication
targets for AD treatment, these molecular pathways hub genes will be helpful.

A new class of paracompactness in the nano topological spaces, termed nano pre open sets, are
presented and explored in this article. Since the nano topology contains at most five sets this leads us to establish new structures of nano open sets, nano open covers, and nano locally refinement coves new requirement concepts are discussed like nano pre open covers, nano pre ????0,????1, ????2, and nano pre- regular, nano pre-normal spaces, and
countable nano pre-open paracompact. Many new theorems are stated and proved.

In many practical fields, such as engineering, physics, chemistry, biology, psychology, economics, and
finance, processes are simulated using differential equations. These models solutions, in contrast to algebraic
equations, may be more intricate. In order to get at the solutions to these models, it is easy to employ integral
transformations. In this paper, we use the Upadhyaya transform to obtain accurate solutions to two cardiovascular
models. It is obvious that the Upadhyaya transform is an effective, dependable, and simple technique for solving
differential equations.

A (n,r)-arc ???? in a projective plane PG(2,q) is a set of n points such that some r, but no r+1 of them, are
collinear. A (n,r)-arc ???? is called complete if it is not contain in a (n+1,r)-arc. A linear [????, ????, ????]????-code ???? over a finite
field ???????? is a k-dimensional subspace of ????????
????
with minimum hamming distance d and length n. A code with parameters
[????????(????, ????), ????, ????]
????
with Griesmer bound ????????(????, ????), is called Griesmer code. The major aim of this research is to find
large size for the complete (k,3)-arcs in the projective plane of order nineteen PG(2,19) using the method of secants
distributions, and the disjoint union of arcs, as well as, adding and removing points to (from) particular conic
respectively. Also, we find the Griesmer codes that correspond to each large complete (k,3)-arcs, k=29,30,31. We
introduced 20 inequivalent (29,3)-arcs up to secant distribution, 10 of them are complete. Also, we introduced 8
inequivalent (30,3)-arcs up to secant distribution, 2 of them are complete. Moreover, we construct 3 inequivalent
complete (31,3)-arcs up to secant distribution, and then find the corresponding linear codes to some of the (29,3)arcs,

(30,3)-arcs and (31,3)-arcs. In particular, we established 3 types of Griesmer codes, and we find the weight
enumerator that correspond to each one of them.

Multiple linear regression modeling was used to analyze Covid-19 data, which represents the number
of infections in Iraq for the year 2019, in order to find occupational discrepancies between the dependent variable
(age) and the independent factors under discussion. This was carried out in addition to the correlation value.
Following statistical analysis, a significant correlation was discovered between the independent factors and the
dependent variable, age. The age dependent variable and the research's independent variables are evidently different
from one another in a substantial degree, as indicated by the analysis of variance table. This is in addition to
comparing the number of infections between boys and females for each of the study's variables (blood pressure,
oxygen rate, sugar rate, and D-Dimer), and we discovered that there are no appreciable variations in the quantity of
infections between males and females based on the factorial experiment analysis.

This work discusses a new description of Picard’s iterative method (PIM) to get the approximate or
sometimes exact solution of (linear and nonlinear) partial differential equations ,Provided that by examples to
illustrate the reliability and ease of this method.

There are numerous uses for fractional differential equations in engineering, physics, and technology.
A path for solving the fractal differential equations was examined, and its homogeneous form of ????
???????? + ???????? = 0 was introduced. The notions of Riemann-Liouville fractional derivatives served as the foundation for the journey.. The solutions of the linear non-homogeneous fractal differential equations are given in detail.

In this work, we compute the decomposition matrix to the spin characteristics of S_28 for a given field
of characteristic p=11, the connections between the irreducible modular spin characters and the irreducible spin
characters of S_28. The technique employed in this study is (r,r ̅ )-inducing, which creates projective characters for
S_28 by using the projective characters of S_27. Maple was used to seeing all available columns and then choosing
the potentially appropriate columns of them. In order to explore irreducible modular spin characteristics, general
correlations and theorems will be discovered as a result of this research.

Elliptic Curve Cryptosystem, which offers a high level of security with a reduced key size, has emerged
as the best option for public key encryption. Elliptic curve cryptosystem has proven to be the best solution for public
key encryption, where it provides a good level of security with smaller key size. In this paper, we attempt to develop
an enhanced image encryption algorithms based on ECC by use two keys as circulant matrix in one of them, while
generation another key from simple linear system modulo to purpose of image cryptography. The results of the
suggested algorithm comparison with recent research are used to assess it where results were better than previous
works

The operational range of conventional and license-free radio-controlled drones is limited due to
line-of-sight restrictions (LoS). There exists a definitive method for operating a drone. Consequently, in order to
fly the drone beyond the visual line of sight (BVLoS), it is necessary to replace the drone's original wireless
communications equipment with a device that requires a licence and is connected to a cellular network. LongTerm
Evolution
(LTE),
a
terrestrial
communication
technique,
enables
a
drone
to
establish
a
real-time
connection

with

a ground station. This connection serves the goals of command and control (C&C) as well as payload
delivery. Nevertheless, it is important to note that the electromagnetic environment undergoes changes as altitude
increases, which can potentially complicate the process of interfacing with drones over terrestrial cellular
networks. The objective of this article is to develop a prototype control system for low-altitude microdrones using
LTE technology. Additionally, it seeks to assess the feasibility and effectiveness of cellular connectivity for drones
operating at various altitudes. This evaluation will be conducted by examining factors like as latency, handover,
and signal strength. At a certain altitude, the received signal experiences a decrease in power level by 20 dBm
and a degradation in signal quality by 10 dB. The data throughput of the downlink had a fall of 70%, while the
latency exhibited an increase of 94 ms. Despite meeting the basic criteria for drone cellular connection, the
existing LTE network necessitates enhancements in order to expand aerial coverage, mitigate interference, and
minimise network latency.

The class of D(T)- operators are equivalent to the class of quasi-normal operators. This paper
discusses additional properties of this class of operators. Assuming that if the operator T is not far from normality
and U serves as an interrupter, it follows that the operator U will be both unique and positive. Moreover, we explore
other properties that merge when the operator T commutes with T^* T. In one of our main theorems, we demonstrate
that the operator T in the class D(T) is also normal when it is invertible.

In this ????????????????????, ????ℎ???? ????????????cepts of (????, ????) − ???????????????????????????????????? ???????????????????????????????????????????? of fuzzy R???? − ????????????algebras and (????, ????)
????????????????????????????????d t????????????????????ation fuz???????? ???? − ????????????als of R???? − ????????????????????????as are given, some properties and some examples that
illustrate certain cases, such as reverse some of the theorems and others, on R???? − ????????????????????????ebra and q-ideals, each of
which had its own proofs, characteristics and relationships.

Abstrac????. ????e consi???????????? ????ℎ???? ???????????????????? ????????????????????ion of tℎ???? ???????????????????????????? ???????????????????? ???????????? ????????????e funda???????????????????????? ????????????????????????????????????s to
RG-a???????????????????????? ????re dis???????????????????????? ???????????? ????ℎ???? ???????????????????? (???????????? − ????????????ge) of ???????????????????? ???????? ???????? − ????????????????bra, and ????????????????????????????????????????????
???????????????? ???????? ????ℎ???????????? ????????????????erties and inv???????????????????????????????? ???????????????? ???????????????????????????? ????????????????????rties.