Journal of Applied Analysis and Computation

Papers
(The TQCC of Journal of Applied Analysis and Computation is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-05-01 to 2025-05-01.)
ArticleCitations
THE DYNAMIC EFFECTS OF DIFFERENT QUARANTINE MEASURES ON THE SPREAD OF COVID-1963
ON EPIDEMIOLOGICAL TRANSITION MODEL OF THE EBOLA VIRUS IN FRACTIONAL SENSE42
EXECUTION OF A NOVEL DISCRETIZATION APPROACH FOR SOLVING VARIABLE-ORDER CAPUTO-RIESZ TIME-SPACE FRACTIONAL SCHRÖDINGER EQUATIONS21
QUALITATIVE ANALYSIS OF HIGH-DIMENSIONAL NEURAL NETWORKS WITH THREE-LAYER STRUCTURE AND MUTIPLE DELAYS12
EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATION WITH INFINITE-POINT BOUNDARY VALUE CONDITIONS10
A HYBRID SWITCHING S-DI-A EPIDEMIC MODEL WITH STANDARD INCIDENCE: PERSISTENCE, EXTINCTION AND POSITIVE RECURRENCE8
NUMERICAL METHODS FOR THE CAPUTO-TYPE FRACTIONAL DERIVATIVE WITH AN EXPONENTIAL KERNEL7
BIFURCATIONS OF DOUBLE HETERODIMENSIONAL CYCLES WITH THREE SADDLE POINTS7
A NEW EFFICIENT TRANSFORM MECHANISM WITH CONVERGENCE ANALYSIS OF THE SPACE-FRACTIONAL TELEGRAPH EQUATIONS6
EXISTENCE AND UNIQUENESS OF CONSTRAINED MINIMIZERS FOR FRACTIONAL KIRCHHOFF TYPE PROBLEMS IN HIGH DIMENSIONS5
CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM5
DYNAMICAL BEHAVIORS OF A DISCRETE-TIME PREY-PREDATOR MODEL WITH HARVESTING EFFECT ON THE PREDATOR5
THE NUMBER OF LIMIT CYCLES FROM ELLIPTIC HAMILTONIAN VECTOR FIELDS BY HIGHER ORDER MELNIKOV FUNCTIONS5
FINITE-TIME STABILITY OF DISCRETE DESCRIPTOR SYSTEMS WITH TIME-VARYING DELAY AND NONLINEAR UNCERTAINTIES5
DYNAMICS OF A STOCHASTIC VECTOR-HOST EPIDEMIC MODEL WITH AGE-DEPENDENT OF VACCINATION AND DISEASE RELAPSE4
EXISTENCE AND ASYMPTOTIC BEHAVIOR OF GROUND STATE SOLUTIONS FOR A CLASS OF MAGNETIC KIRCHHOFF CHOQUARD TYPE EQUATION WITH A STEEP POTENTIAL WELL4
IMPROVEMENT OF THE SPECTRAL METHOD FOR SOLVING MULTI-TERM TIME-SPACE RIESZ-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS4
PLANAR INTEGRABLE NONLINEAR OSCILLATORS HAVING A STABLE LIMIT CYCLE4
HOPF BIFURCATION IN A PREDATOR-PREY MODEL WITH MEMORY EFFECT AND INTRA-SPECIES COMPETITION IN PREDATOR4
INVERSE VARIATIONAL PRINCIPLES FOR TOPOLOGICAL PRESSURES ON MEASURES4
ASYMPTOTIC BEHAVIORS OF A HEROIN EPIDEMIC MODEL WITH NONLINEAR INCIDENCE RATE INFLUENCED BY STOCHASTIC PERTURBATIONS3
HYPERSTABILITY RESULTS FOR GENERALIZED QUADRATIC FUNCTIONAL EQUATIONS IN <inline-formula><tex-math id="M1">$(2,\alpha)$</tex-math></inline-formula>-BANACH SPACES3
THE BEST MATCHING PARAMETERS AND NORM CALCULATION OF BOUNDED OPERATORS WITH SUPER-HOMOGENEOUS KERNEL3
PSI, POLYGAMMA FUNCTIONS AND <i>Q</i>-COMPLETE MONOTONICITY ON TIME SCALES3
INFLUENCE OF INITIAL RAMP ON CONVOLUTIONAL NONVISCOUS DAMPING MATERIALS3
OSCILLATION OF SECOND-ORDER HALF-LINEAR NEUTRAL NONCANONICAL DYNAMIC EQUATIONS3
BIFURCATIONS OF TRAVELING WAVE SOLUTIONS IN THE HOMOGENEOUS CAMASSA-HOLM TYPE EQUATIONS3
HOPF BIFURCATION AND CHAOS OF COMBINATIONAL IMMUNE ANTI-TUMOR MODEL WITH DOUBLE DELAYS3
ANALYSIS OF A DEGENERATED DIFFUSION SVEQIRV EPIDEMIC MODEL WITH GENERAL INCIDENCE IN A SPACE HETEROGENEOUS ENVIRONMENT3
DYNAMICS ANALYSIS OF THREE-SPECIES REACTION-DIFFUSION SYSTEM VIA THE MULTIPLE SCALE PERTURBATION METHOD3
THE DYNAMICAL BEHAVIOR AND PERIODIC SOLUTION IN DELAYED NONAUTONOMOUS CHEMOSTAT MODELS3
CONVERGENCE OF THE TWO-POINT MODULUS-BASED MATRIX SPLITTING ITERATION METHOD3
A NEW NUMERICAL TECHNIQUE FOR INVESTIGATING BOUNDARY VALUE PROBLEMS WITH Ψ-CAPUTO FRACTIONAL OPERATOR3
ELZAKI TRANSFORM BASED ACCELERATED HOMOTOPY PERTURBATION METHOD FOR MULTI-DIMENSIONAL SMOLUCHOWSKI'S COAGULATION AND COUPLED COAGULATION-FRAGMENTATION EQUATIONS3
ALMOST-PERIODIC BIFURCATIONS FOR 2-DIMENSIONAL DEGENERATE HAMILTONIAN VECTOR FIELDS3
STATIONARY DISTRIBUTION AND PERMANENCE OF A STOCHASTIC DELAY PREDATOR-PREY LOTKA-VOLTERRA MODEL WITH LÉVY JUMPS2
SOLVING THE YANG-BAXTER-LIKE MATRIX EQUATION FOR A RANK-ONE MATRIX2
HOPF BIFURCATION IN THE DELAYED FRACTIONAL LESLIE-GOWER MODEL WITH HOLLING TYPE II FUNCTIONAL RESPONSE2
EFFECT OF NONLOCAL DELAY WITH STRONG KERNEL ON VEGETATION PATTERN2
SUBORDINATIONS BY CERTAIN UNIVALENT FUNCTIONS ASSOCIATED WITH A FAMILY OF MULTIPLIER TRANSFORMATIONS2
BOUNDEDNESS CRITERION FOR SUBLINEAR OPERATORS AND COMMUTATORS ON GENERALIZED MIXED MORREY SPACES2
HOPF BIFURCATION AND CONTROL FOR THE DELAYED PREDATOR-PREY MODEL WITH NONLINEAR PREY HARVESTING2
CONTINUITY OF SOLUTIONS IN <inline-formula><tex-math id="M1">$ H^1( {\mathbb{R}}^N)\cap L^{p}( {\mathbb{R}}^N) $</tex-math></inline-formula> FOR STOCHASTIC REACTION-DIFFUSION E2
FLIP BIFURCATION WITH RANDOM EXCITATION2
ANALYTICAL INTEGRABILITY OF PERTURBATIONS OF DEGENERATE QUADRATIC SYSTEMS2
UNIVERSAL APPROACH TO THE TAKESAKI-TAKAI <inline-formula><tex-math id="M1">$\gamma $</tex-math></inline-formula>-DUALITY2
DECAY PROPERTIES AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS FOR THE NONLINEAR FRACTIONAL SCHRÖDINGER-POISSON SYSTEM2
ANALYTICAL AND NUMERICAL DISCUSSION FOR THE PHASE-LAG VOLTERRA-FREDHOLM INTEGRAL EQUATION WITH SINGULAR KERNEL2
STABILIZED PRIMAL AND DUAL HYBRID MIXED DGFEM FOR DARCY FLOW2
GREEN FUNCTION OF A CLASS OF EIGENPARAMETER DEPENDENT THIRD-ORDER DIFFERENTIAL OPERATORS WITH DISCONTINUITY2
MULTIPLICITY OF SOLUTIONS FOR FRACTIONAL <i>κ</i>(<i>X</i>)-LAPLACIAN EQUATIONS2
ORBITAL STABILITY OF SOLITARY WAVES FOR THE NONLINEAR SCHRÖDINGER-KDV SYSTEM2
BIFURCATIONS AND EXACT TRAVELING WAVE SOLUTIONS FOR THE GENERALIZED NONLINEAR SCHRÖDINGER EQUATION WITH WAVE OPERATOR2
STABILITY OF TRAVELING WAVE FRONTS FOR NONLOCAL DIFFUSIVE SYSTEMS2
MULTIPLE SOLUTIONS FOR A CLASS OF MODIFIED QUASILINEAR FOURTH-ORDER ELLIPTIC EQUATIONS2
EXISTENCE OF KINK WAVES TO PERTURBED DISPERSIVE K(3, 1) EQUATION2
STUDIES ON PULL-IN INSTABILITY OF AN ELECTROSTATIC MEMS ACTUATOR: DYNAMICAL SYSTEM APPROACH2
SOME RESULTS ON VALUE DISTRIBUTION OF MEROMORPHIC FUNCTIONS CONCERNING DIFFERENCE POLYNOMIALS2
AFFINE-PERIODIC SOLUTIONS FOR PERTURBED SYSTEMS2
SOLVABILITY FOR A HIGHER-ORDER HADAMARD FRACTIONAL DIFFERENTIAL MODEL WITH A SIGN-CHANGING NONLINEARITY DEPENDENT ON THE PARAMETER <inline-formula><tex-math id="M1">$\varrho$</tex-math&2
NEW OSCILLATION CRITERIA FOR A CLASS OF HIGHER-ORDER NEUTRAL FUNCTIONAL DYNAMIC EQUATIONS ON TIME SCALES2
AN EFFECTIVE SUSTAINABLE COLLOCATION METHOD FOR SOLVING REGULAR/SINGULAR SYSTEMS OF CONFORMABLE DIFFERENTIAL EQUATIONS SUBJECT TO INITIAL CONSTRAINT CONDITIONS1
GLOBAL EXISTENCE AND CONTINUOUS DEPENDENCE ON PARAMETERS OF CONFORMABLE PSEUDO-PARABOLIC INCLUSION1
NON-HOMOGENEOUS REACTION IN A NON-LINEAR DIFFUSION OPERATOR WITH ADVECTION TO MODEL A MASS TRANSFER PROCESS1
SOLITON, BREATHER AND LUMP MOLECULES IN THE (2+1)-DIMENSIONAL B-TYPE KADOMTSEV-PETVIASHVILI-KORTEWEG DE-VRIES EQUATION1
SOLUTIONS OF THE YANG-BAXTER-LIKE MATRIX EQUATION FOR THE MATRIX WITH NONSINGULAR JORDAN BLOCKS1
DYNAMICS OF A TWO-PATCH NICHOLSON'S BLOWFLIES MODEL WITH RANDOM DISPERSAL1
INDIRECT BOUNDARY STABILIZATION FOR WEAKLY COUPLED DEGENERATE WAVE EQUATIONS UNDER FRACTIONAL DAMPING1
LACUNARY STATISTICAL HARMONIC SUMMABILITY1
DEGENERATION OF LUMP-TYPE LOCALIZED WAVES IN THE (2+1)-DIMENSIONAL ITO EQUATION1
DYNAMICAL BEHAVIORS OF A TUMOR-IMMUNE-VITAMIN MODEL WITH RANDOM PERTURBATION1
A NEW NUMERICAL TECHNIQUE FOR SOLVING <i>ψ</i>-FRACTIONAL RICCATI DIFFERENTIAL EQUATIONS1
EXISTENCE AND CONTROLLABILITY FOR IMPULSIVE FRACTIONAL STOCHASTIC EVOLUTION SYSTEMS WITH STATE-DEPENDENT DELAY1
SPECTRAL-GALERKIN APPROXIMATION BASED ON REDUCED ORDER SCHEME FOR FOURTH ORDER EQUATION AND ITS EIGENVALUE PROBLEM WITH SIMPLY SUPPORTED PLATE BOUNDARY CONDITIONS1
ATTRACTORS FOR RANDOM LATTICE DYNAMICAL SYSTEMS WITH INFINITE MULTIPLICATIVE COLORED NOISE1
EVOLUTIONARY BEHAVIOR OF THE INTERACTION SOLUTIONS FOR A (3+1)-DIMENSIONAL GENERALIZED BREAKING SOLITON EQUATION1
NONEXISTENCE OF STABLE SOLUTIONS OF THE WEIGHTED LANE-EMDEN SYSTEM1
PROPAGATING TERRACE IN A PERIODIC REACTION-DIFFUSION EQUATION WITH CONVECTION1
SUPER-CRITICAL PROBLEMS INVOLVING THE FRACTIONAL <inline-formula><tex-math id="M1">$P$</tex-math></inline-formula>-LAPLACIAN1
A NEW NUMERICAL APPROACH OF SOLVING FRACTIONAL MOBILE-IMMOBILE TRANSPORT EQUATION USING ATANGANA-BALEANU DERIVATIVE1
OPTIMAL CONTROL OF TUMOR-LYMPHATIC MODEL WITH IMMUNO-CHEMOTHERAPY1
DYNAMICAL BEHAVIOR OF THE FECAL-ORAL TRANSMISSION DISEASES MODEL ON A <i>T</i>-PERIODIC EVOLUTION DOMAIN1
FRACTIONAL MEYER NEURAL NETWORK PROCEDURES OPTIMIZED BY THE GENETIC ALGORITHM TO SOLVE THE BAGLEY-TORVIK MODEL1
<i>P</i>-DISTRIBUTION ALMOST PERIODIC SOLUTIONS OF SEMI-LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH <i>G</i>-BROWNIAN MOTION1
BÄCKLUND TRANSFORMATION TO SOLVE THE GENERALIZED (3+1)-DIMENSIONAL KP-YTSF EQUATION AND KINKY PERIODIC-WAVE, WRONSKIAN AND GRAMMIAN SOLUTIONS1
PERIODIC DISCRETE NONLINEAR SCHRÖDINGER EQUATIONS WITH PERTURBED AND SUB-LINEAR TERMS1
SOME NOVEL INERTIAL BALL-RELAXED CQ ALGORITHMS FOR SOLVING THE SPLIT FEASIBILITY PROBLEM WITH MULTIPLE OUTPUT SETS1
LIE SYMMETRY, EXACT SOLUTIONS AND CONSERVATION LAWS OF SOME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS1
STUDIES ON THE INTERACTION MECHANISM BETWEEN THE MRNA VACCINE AGAINST SARS-COV-2 AND THE IMMUNE SYSTEM1
STABILITY AND EXISTENCE OF SOLUTIONS FOR A COUPLED SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS1
AN EFFICIENT WAVELET COLLOCATION METHOD BASED ON HERMITE POLYNOMIALS FOR A CLASS OF 2D QUASI-LINEAR ELLIPTIC EQUATIONS1
ON A SUPERLINEAR SECOND ORDER ELLIPTIC PROBLEM AT RESONANCE1
HOPF BIFURCATION PROBLEM FOR A CLASS OF KOLMOGOROV MODEL WITH A POSITIVE NILPOTENT CRITICAL POINT1
EXISTENCE OF THE GENERALIZED EXPONENTIAL ATTRACTOR FOR COUPLED SUSPENSION BRIDGE EQUATIONS WITH DOUBLE NONLOCAL TERMS1
EXTINCTION AND STATIONARY DISTRIBUTION OF A STOCHASTIC PREDATOR-PREY MODEL WITH HOLLING Ⅱ FUNCTIONAL RESPONSE AND STAGE STRUCTURE OF PREY1
PULLBACK EXPONENTIAL ATTRACTORS FOR NON-AUTONOMOUS ABSTRACT RETARDED EVOLUTION EQUATIONS1
ALLEN-CAHN EQUATION BASED ON AN UNCONSTRAINED ORDER PARAMETER WITH SOURCE TERM AND ITS CAHN-HILLIARD LIMIT1
ON RESONANT FRACTIONAL <i>Q</i>-DIFFERENCE SCHRÖDINGER EQUATIONS1
ON A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY WITH THE MULTIPLE UPPER LIMIT FUNCTION AND THE PARTIAL SUMS1
BILINEAR <inline-formula><tex-math id="M1">$\Theta$</tex-math></inline-formula>-TYPE CALDERÓN-ZYGMUND OPERATOR AND ITS COMMUTATOR ON PRODUCT NON-HOMOGENEOUS GENERALIZED MORREY 1
B<i>Ä</i>CKLUND TRANSFORMATIONS AND ROUGE WAVES IN THE FRAME OF A FRACTIONAL ORDER MODEL IN MAGNETIZED DUSTY PLASMA1
ANALYTICALLY EXPLICIT INVERSE OF A KIND OF PERIODIC TRIDIAGONAL MATRIX USING A BACKWARD CONTINUED FRACTION APPROACH1
MULTIPLE SOLUTIONS FOR NONHOMOGENEOUS KLEIN-GORDON EQUATION WITH SIGN-CHANGING POTENTIAL COUPLED WITH BORN-INFELD THEORY1
LIE SYMMETRIES, GROUP INVARIANT SOLUTIONS AND CONSERVATION LAWS OF IDEAL MHD EQUATIONS1
EFFICACY OF THE RICE CROP GROWTH USING DIFFERENT SMOOTHING METHODS1
SUCCESSIVE ITERATIONS FOR POSITIVE EXTREMAL SOLUTIONS OF BOUNDARY VALUE PROBLEMS ON THE HALF-LINE1
HERMITE–HADAMARD TYPE INEQUALITIES FOR KATUGAMPOLA FRACTIONAL INTEGRALS1
GLOBAL EXISTENCE AND BLOW-UP PHENOMENA FOR THE DOUBLY NONLINEAR DIFFUSION EQUATION WITH NONLINEAR NEUMANN BOUNDARY CONDITIONS1
BIFURCATIONS AND EXACT SOLUTIONS OF THE OPTICAL SOLITON MODEL IN METAMATERIALS DOMINATED BY ANTI-CUBIC NONLINEARITY1
AN EXTENSIONAL CONFORMABLE FRACTIONAL DERIVATIVE AND ITS EFFECTS ON SOLUTIONS AND DYNAMICAL PROPERTIES OF FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS1
ON THE INVARIANCE OF GENERALIZED QUASIARITHMETIC MEANS1
ANOTHER IMPROVEMENT ON OSCILLATION CRITERIA FOR FIRST-ORDER DELAY DIFFERENTIAL EQUATIONS1
A TWO-STEP MATRIX SPLITTING METHOD FOR THE MIXED LINEAR COMPLEMENTARITY PROBLEM1
NEW FIXED POINT RESULTS FOR GERAGHTY CONTRACTIONS AND THEIR APPLICATIONS1
OPTIMALITY RESULTS FOR NONDIFFERENTIABLE VECTOR OPTIMIZATION PROBLEMS WITH VANISHING CONSTRAINTS1
PARAMETER INDEPENDENT SCHEME FOR SINGULARLY PERTURBED PROBLEMS INCLUDING A BOUNDARY TURNING POINT OF MULTIPLICITY ≥ 11
PARTIAL PERMANENCE AND STATIONARY DISTRIBUTION OF A DELAYED STOCHASTIC FACULTATIVE MUTUALISM MODEL WITH FEEDBACK CONTROLS1
THE NON-EXISTENCE AND EXISTENCE OF NON-CONSTANT POSITIVE SOLUTIONS FOR A DIFFUSIVE AUTOCATALYSIS MODEL WITH SATURATION1
CONTROL DESIGN FOR A CLASS OF GENERAL NONLINEAR REACTION DIFFUSION EQUATIONS1
EXISTENCE OF AT LEAST TWO SOLUTIONS FOR DOUBLE PHASE PROBLEM1
RIEMANN-LIOUVILLE FRACTIONAL INTEGRALS AND DERIVATIVES ON MORREY SPACES AND APPLICATIONS TO A CAUCHY-TYPE PROBLEM1
GLOBAL ASYMPTOTICAL STABILITY FOR A FISHERY MODEL WITH SEASONAL HARVESTING1
BIFURCATIONS OF SOLITARY WAVES, PERIODIC PEAKONS AND COMPACTONS OF A COUPLED NONLINEAR WAVE EQUATION1
AN ALGORITHM FOR NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS USING HARMONY SEARCH AND NEURAL NETWORKS1
PROJECTION SYNCHRONIZATION OF FUNCTIONAL FRACTIONAL-ORDER NEURAL NETWORKS WITH VARIABLE COEFFICIENTS1
EXISTENCE OF PERIODIC SOLUTIONS FOR TWO CLASSES OF SECOND ORDER <inline-formula><tex-math id="M1">$ P $</tex-math></inline-formula>-LAPLACIAN DIFFERENTIAL EQUATIONS1
UNIQUENESS OF STEADY STATE POSITIVE SOLUTIONS TO A GENERAL ELLIPTIC SYSTEM WITH DIRICHLET BOUNDARY CONDITIONS1
A MIXED-TYPE PICARD-S ITERATIVE METHOD FOR ESTIMATING COMMON FIXED POINTS IN HYPERBOLIC SPACES1
MULTIPLE PERIODIC SOLUTIONS FOR SUPERQUADRATIC AND SUBQUADRATIC SECOND-ORDER HAMILTONIAN SYSTEMS1
SPECTRA OF GRAPH OPERATIONS BASED ON SPLITTING GRAPH1
THE SEIR MODEL WITH PULSE AND DIFFUSION OF VIRUS IN THE ENVIRONMENT1
A ACCELERATED MODIFIED SHIFT-SPLITTING METHOD FOR NONSYMMETRIC SADDLE POINT PROBLEMS1
SOLVABILITY OF SOME RIEMANN-HILBERT PROBLEMS RELATED TO DIRAC OPERATOR WITH GRADIENT POTENTIAL IN <inline-formula><tex-math id="M1">$\mathbb{R}^3$</tex-math></inline-formula>1
PARTIAL-APPROXIMATE CONTROLLABILITY OF HILFER FRACTIONAL BACKWARD EVOLUTION SYSTEMS1
THE EFFECT OF AN ADDITIVE NOISE ON SOME SLOW-FAST EQUATION NEAR A TRANSCRITICAL POINT1
NUMERICAL AND MATHEMATICAL ANALYSIS OF A NONLINEAR SCHRÖDINGER PROBLEM WITH MOVING ENDS1
HIGHER ORDER EXPANSIONS IN FINITE ION SIZE VIA POISSON-NERNST-PLANCK SYSTEMS WITH BIKERMAN'S LOCAL HARD-SPHERE POTENTIAL1
A NOVEL TECHNIQUE FOR SOLVING (2+1) DIMENSIONAL SYSTEM OF NONLINEAR COUPLED PARTIAL DIFFERENTIAL EQUATION1
VIRTUAL ELEMENT APPROXIMATIONS FOR NON-STATIONARY NAVIER-STOKES EQUATIONS ON POLYGONAL MESHES1
NUMERICAL SOLUTION AND OPTIMAL CONTROL FOR FRACTIONAL TUMOR IMMUNE MODEL1
THE SECOND-ORDER DIFFERENTIAL EQUATION METHOD FOR SOLVING THE VARIATIONAL INEQUALITY PROBLEM1
EXPLICIT SOLUTIONS TO A HIERARCHY OF DISCRETE COUPLING KORTEWEG-DE VRIES EQUATIONS1
RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC WAVE EQUATIONS WITH STRONG DAMPING AND ADDITIVE NOISE ON <inline-formula><tex-math id="M1">$ {\mathbb{R}}^{N} $</tex-math></inline1
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