1.
A* *Brief* *Parametric* *Analysis* **of** *Catastrophic* *or* *Disastrous* *Hurricanes* *That* *Have* *Hit* *the* *Florida* *Keys* *between* *1900* *and* *2000

摘要：The* *most* *intense* *and* *catastrophic* *hurricanes* *on* *record
to* *hit* *the* *Florida* *Keys* *during* *1900* *to* *1950* *were* *in* *1919,* *and* *1935.* *From* *1950* *to
2000,* *the* *most* *intense* *hurricanes* *to* *hit* *or* *affect* *the* *Florida* *Keys* *were* *in* *1960,
1965,* *and* *1992.* *In* *this* *paper,* *we* *will* *present* *a* *brief* *parametric* *analysis* **of** *the
hurricanes* *that* *have* *hit* *the* *Florida* *Keys* *in* *the* *last* *100* *years.* *This* *analysis* *will
include* *the* *descriptive* *statistics,* *best* *fit* *probability* *distribution* **of** *the* *latitude
*of** *the* *catastrophic* *hurricanes* *and* *a* *confidence* *interval* *that* *detects* *the* *average
latitude* **of** *hurricanes* *(category* *3* *or* *higher)* * style="font-family:Verdana;">which style="font-family:Verdana;">* *have* *hit
the* *Florida* *Keys* *in* *the* *last* *100* *years....

摘要：A* *topological* *structural
design* *approach* *is* *presented* *which* *is* *based* *upon* *the* *implementation* **of** *a* *two
phase* *evolutionary* *optimization* *algorithm* *in* *conjunction* *with* *a* *finite* *element
analysis* *code.* *The* *first* *phase* *utilizes* *a* *conventional* *genetic* * style="font-family:Verdana;">approach* *which* *performs* *a* *global* *search* *for* *the
optimal* *design* *topology.* *Dual* *level* *material* *properties* *are* *specified* *within
the* *genetic* *encoding* *and* *are* *applied* *to* *each* *individual* *element* *in* *the* *design
mesh* *to* *represent* *either* *design* *material* *or* *a* *void.* *The* *second* *phase* *introduces style="font-family:Verdana;">* *a style="font-family:Verdana;">* *rule
based* *refinement* *which* *allows* *for* *user* *design* *intent* *to* *accelerate* *the* *solution
process* *and* *eliminate* *obvious* *design* *discrepancies* *resulting* *from* *the* *phase* *one
search.* *A* *series* **of** *plate* *design* *problems* *are* *presented* *where* *the* *objective* *is
to* *minimize* *the* *overall* *volume* **of** *the* *structure* *under* *predefined* *loading* *and
constraint* *conditions.* *The* *constraints* *include* *both* *stress* *and* *deflection
considerations* *where* *stress* *is* *calculated* *through* *the* *use* **of** *a* *commercial
finite* *element* *package.* *The* *initial* *plate* *example* *incorporates* *a* *coarse* *mesh,
but* *a* *gradual* *decrease* *in* *element* *size* *was* *employed* *for* *the* *remaining* *cases
examined.* *Replacement* **of** *the* *phase* *one* *search* *with* *a* *set* **of** *randomly* *generated
designs* *is* *demonstrated* *in* *order* *to* *form* *a* *greatly* *reduced* *design* *space* *which
drastically* *increases* *the* *efficiency* **of** *the* *solution* *process.* *Comparison
results* *are* *drawn* *between* *the* *conventional* *genetic* *algorithm* *and* *the* *two* *phase
procedure....

3.
Magnetohydrodynamic* *Casson* *Fluid* *Flow* *over* *an* *Infinite* *Vertical* *Plate* *with* *Chemical* *Reaction* *and* *Heat* *Generation

摘要：

... style="text-align:justify;">
In* *this* *paper,* *the* *fluid* *examined* *was* *electrically* *conducting.* *The* *presence* **of*
a* *uniform* *transverse* *magnetic* *field* *at* *the* *plate* *was* *also* *taken* *into* *cognizance.
The* *flow* *was* *governed* *by* *a* *modeled* *coupled* *nonlinear* *system* **of** *partial
differential* *equations* *(PDEs)* *in* *dimensional* *form* *which* *was* *transformed
into* *non-dimensional* *form* *using* *some* *non-dimensional* *variables.
Explicit* *finite* *difference* *method* *(EFDM)* *was* *employed* *to* *approximate* *the
fluid* *velocity,* *temperature* *and* *concentration.* *The* *effects* **of** *embedded
thermo* *physical* *parameters* **of** *engineering* *interests* *on* *the* *flow* *quantities
viz.* *velocity,* *temperature,* *concentration* *field* *presented* *through* *graphs* *were
also* *examined* *through* *a* *series* **of** *numerical* *experiments* *and* *discussed.
During* *the* *course* **of** *the* *numerical* *computations,* *it* *was* *found* *that* *heat
generation* *has* *a* *tendency* *to* *enhance* *the* *fluid* *velocity* *as* *an* *opposite* *result
is* *seen* *with* *chemical* *reaction* *parameter.* *A* *comparison* *was* *conducted* **of*
present* *results* *with* *the* *previous* *literature* *to* *show* *the* *accuracy* **of** *the* *results.

4.
Erratum* *to* *“Simple* *Method* *for* *Evaluating* *Singular* *Integrals”* *[*American** **Journal** **of** **Computational** **Mathematics*,* *Volume* *7,* *Number* *4,* *December* *2017* *PP.* *444-450]

摘要：

... style="text-align:justify;">
In* *this* *paper,* *we* *study* *the* *class* **of** *one-dimensional* *singular* *integrals* *that
converge* *in* *the* *sense* **of** *Cauchy* *principal* *value.* *In* *addition,* *we* *present* *a
simple* *method* *for* *approximating* *such* *integrals.

摘要：

... style="text-align:justify;">
A* *Fast* *Fourier* *transform* *approach* *has* *been* *presented* *by* *Carr* *&* *Madan
(2009)* *on* *a* *single* *underlying* *asset.* *In* *this* *current* *research* *paper,* *we
present* *fast* *Fourier* *transform* *algorithm* *for* *the* *valuation* **of** *Multi-asset
Options* *under* *Economic* *Recession* *Induced* *Uncertainties.* *The* *issue* **of** *multi-dimension* *in* *both* *finite* *and* *infinite* *case* **of** *Options* *is* *part* **of** *the* *focus* **of*
this* *research.* *The* *notion* **of** *economic* *recession* *was* *incorporated.* *An
intuition* *behind* *the* *introduction* **of** *recession* *induced* *volatility* *uncertainty
is* *revealed* *by* *huge* *volatility* *variation* *during* *the* *period* **of** *economic* *recession
compared* *to* *the* *period* **of** *recession-free.* *Nigeria* *economic* *recession
outbreak* *in* *2016* *and* *its* *effects* *on* *the* *uncertainty* **of** *the* *payoffs* **of** *Nigeria
Stocks* *Exchange* *(NSE)* *among* *other* *investments* *was* *among* *the* *motivating
factors* *for* *proposing* *economic* *recession* *induced* *volatility* *in* *options* *pricing.
The* *application* **of** *the* *proposed* *Fast* *Fourier* *Transform* *algorithm* *in
handling* *multi-assets* *options* *was* *shown.* *A* *new* *result* *on* *options* *pricing
was* *achieved* *and* *capable* **of** *yielding* *efficient* *option* *prices* *during* *and* *out* **of*
recession.* *Numerical* *results* *were* *presented* *on* *assets* *in* *3-dimensions* *as* *an
illustration* *taking* *Black* *Scholes* *prices* *as* *a* *bench* *mark* *for* *method* *effectiveness
comparison.* *The* *key* *findings* **of** *this* *research* *paper* *among* *other* *crucial
contributions* *could* *be* *seen* *in* **computational** *procedure* **of** *options* *valuation
in* *multi-dimensions* *and* *uncertainties* *in* *options* *payoffs* *under* *the* *exposure
*of** *economic* *recession.

摘要：

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We* *develop* *a* *dynamical* *model* *to* *understand* *the* *underlying* *dynamics* **of*
TUBERCULOSIS* *infection* *at* *population* *level.* *The* *model,* *which* *integrates
the* *treatment* **of** *individuals,* *the* *infections* **of** *latent* *and* *recovery* *individuals,
is* *rigorously* *analyzed* *to* *acquire* *insight* *into* *its* *dynamical* *features.* *The
phenomenon* *resulted* *due* *to* *the* *exogenous* *infection* **of** *TUBERCULOSIS
disease.* *The* *mathematical* *analysis* *reveals* *that* *the* *model* *exhibits* *a* *backward
bifurcation* *when* *TB* *treatment* *remains* **of** *infected* *class.* *It* *is* *shown* *that,* *in
the* *absence* **of** *treatment,* *the* *model* *has* *a* *disease-free* *equilibrium* *(DEF)
which* *is* *globally* *asymptotically* *stable* *(GAS)* *and* *the* *associated* *reproduction
threshold* *is* *less* *than* *unity.* *Further,* *the* *model* *has* *a* *unique* *endemic* *equilibrium
(EEP),* *for* *a* *special* *case,* *whenever* *the* *associated* *reproduction* *threshold
quantity* *exceeds* *unity.* *For* *a* *special* *case,* *the* *EEP* *is* *GAS* *using* *the
central* *manifold* *theorem* **of** *Castillo-Chavez.

摘要：

... style="text-align:justify;">
We* *present* *a* *fourth-order* *finite* *difference* *scheme* *for* *the* *Helmholtz* *equation
in* *polar* *coordinates.* *We* *employ* *the* *finite* *difference* *format* *in* *the* *interior
*of** *the* *region* *and* *derive* *a* *nine-point* *fourth-order* *scheme.* *Specially,
ghost* *points* *outside* *the* *region* *are* *applied* *to* *obtain* *the* *approximation* *for
the* *Neumann* *boundary* *condition.* *We* *obtain* *the* *matrix* *form* **of** *the* *linear
system* *and* *the* *sparsity* **of** *the* *coefficient* *matrix* *is* *favorable* *for* *the* *computation
*of** *the* *Helmholtz* *equation.* *The* *feasibility* *and* *accuracy* **of** *the* *method
are* *validated* *by* *two* *test* *examples* *which* *have* *exact* *solutions.

摘要：

... style="text-align:justify;">
The* *diagnosability* **of** *a* *multiprocessor* *system* *or* *an* *interconnection* *network
is* *an* *important* *research* *topic.* *The* *system* *and* *an* *interconnection* *network
have* *an* *underlying* *topology,* *which* *is* *usually* *presented* *by* *a* *graph.* *In* *this
paper,* *we* *show* *proof* *for* *the* **g*-good-neighbor* *diagnosability* **of** *the* *exchanged
hypercube* **EH** *(s,t)* *under* *the* *PMC* *model* *and* *MM** *model.

摘要：

... style="text-align:justify;">
In* *this* *paper,* *we* *study* *the* *global* *regularity* **of** *the* *classical* *solution* **of** *the* *2*D** *incompressible* *magnetohydrodynamic* *equation* *with* *vertical* *dissipation* *and* *vertical* *magnetic* *dissipation.* *We* *show* *that* *any* *solution* **of** *the* *second* *component* *(u_{2},* *b_{2})* ** *has* *a* *global* *L^{2r}* *-bound,* *where* *r* *satisfies* * src="Edit_c8e493af-5432-4efd-877a-4eeaad6c46fc.jpg"* *width="53"* *height="14"* *alt=""* */>* *and* *the* *boundary* *does* *not* *grow* *faster* *than src="Edit_ab64ca78-7019-4e9b-aa04-8acf4b040145.jpg"* *width="40"* *height="18"* *alt=""* */> as* *r* *increases.

摘要：

... style="text-align:justify;">
In* *this* *paper,* *we* *will* *establish* *a* *formula* *for* *calculating* *the* *3144* *coefficients* *coe(n,* *i)* **of** *the* *first* *hundred* *cyclotomic* **of** *index n* *in* *x^{i}.* *We* *will* *only* *determine* *1003* *for* *an* *index* **n** *odd* *and* *a* *degree* * src="Edit_d01042e4-ce05-4f1a-b86f-92f22d811e94.jpg"* *width="50"* *height="32"* *alt=""* */>* *.* *The* *others* *will* *be* *deduced,* *we’ll* *see* *how.* *The* *formula* *is* * src="Edit_48e2a59f-d74f-42e1-a652-a1462f8eda4e.jpg"* *width="130"* *height="35"* *alt=""* */>* *,* *without* *exception* *if* *u(n)=-1 or* *if* *4* *doesn’t* *divide* * src="Edit_37249895-4092-4e0c-9a4f-25ed03f3b47f.jpg"* *width="40"* *height="23"* *alt=""* */>* *and* *with* *its* *165* *exceptions* **of** *which* *7* *when* *u(n)=0 and* *158* *when* *u(n)=1 that* *will* *be* *shared* *in* *154* *and* *4* *pairs* *(n,* *i),* *which* *we* *will* *specify* *the* *conditions* *and* *values* **of** *the* *coefficients.* *According* *to* *u(n),* *according* *to* *the* *class* **of** *i* *modulo* *p,* *the* *first* *factor* **of** *the* *prime* *factor* *decomposition* **of** *n* *when* *u(n)=1 and* *according* *to* *gcd(n,* *i),* *the* *formula* *will* *or* *will* *not* *be* *valid* *and* *replaced* *otherwise* *by* *the* *good* *value* *that* *will* *be* *0* *for* *152* *pairs* *(n,i)* *or* *1* *in* *the* *13* *other* *exceptions.

11.
Optimal* *Homotopy* *Analysis* **of** *MHD* *Natural* *Convection* *Flow* **of** *Thixotropic* *Fluid* *under* *Subjection* **of** *Thermal* *Stratification:* *Boundary* *Layer* *Analysis

摘要：

... style="text-align:justify;">
In* *this* *article,* *the* *model* **of** *a* *non-Newtonian* *fluid* *(Thixotropic)* *flow* *past* *a* *vertical* *surface* *in* *the* *presence* **of** *exponential* *space* *and* *temperature* *dependent* *heat* *source* *in* *a* *thermally* *stratified* *medium* *is* *studied.* *It* *is* *assumed* *that* *free* *convection* *is* *induced* *by* *buoyancy* *and* *exponentially* *decaying* *internal* *heat* *source* *across* *the* *space.* *The* *dynamic* *viscosity* *is* *taken* *to* *be* *constant* *and* *thermal* *conductivity* **of** *this* *particular* *fluid* *model* *is* *assumed* *to* *vary* *linearly* *with* *temperature.* *Thermal* *stratification* *has* *been* *properly* *incorporated* *into* *the* *governing* *equation* *so* *that* *its* *effect* *can* *be* *revealed* *and* *properly* *reported.* *The* *governing* *partial* *differential* *equations* *describing* *the* *model* *are* *transformed* *and* *parameterized* *to* *a* *system* **of** *non-linear* *ordinary* *differential* *equation* *using* *similarity* *transformations.* *Approximate* *analytic* *solutions* *were* *obtained* *by* *adopting* *Optimal* *Homotopy* *Analysis* *Method* *(OHAM).* *The* *results* *show* *that* *for* *both* *cases* **of** *non-Newtonian* *parameters* *(Thixotropic)* *(K_{1}=K_{2}=0 &* *K_{1}=K_{2}=1.0),* *increasing* *stratification* *parameters,* *relate* *to* *decreasing* *in* *the* *heat* *energy* *entering* *into* *the* *fluid* *region* *and* *thus* *reducing* *the* *temperature* **of** *the* *Thixotropic* *fluid* *as* *it* *flows.

12.
Hybrid* *Numerical* *Method* *with* *Block* *Extension* *for* *Direct* *Solution* **of** *Third* *Order* *Ordinary* *Differential* *Equations

摘要：

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This* *paper* *focuses* *on* *the* *development* **of** *a* *hybrid* *method* *with* *block* *extension* *for* *direct* *solution* **of** *initial* *value* *problems* *(IVPs)* **of** *general* *third-order* *ordinary* *differential* *equations.* *Power* *series* *was* *used* *as* *the* *basis* *function* *for* *the* *solution* **of** *the* *IVP.* *An* *approximate* *solution* *from* *the* *basis* *function* *was* *interpolated* *at* *some* *selected* *off-grid* *points* *while* *the* *third* *derivative* **of** *the* *approximate* *solution* *was* *collocated* *at* *all* *grid* *and* *off-grid* *points* *to* *generate* *a* *system* **of** *linear* *equations* *for* *the* *determination* **of** *the* *unknown* *parameters.* *The* *derived* *method* *was* *tested* *for* *consistency,* *zero* *stability,* *convergence* *and* *absolute* *stability.* *The* *method* *was* *implemented* *with* *five* *test* *problems* *including* *the* *Genesio* *equation* *to* *confirm* *its* *accuracy* *and* *usability.* *The* *rate* **of** *convergence* *(ROC)* *reveals* *that* *the* *method* *is* *consistent* *with* *the* *theoretical* *order* **of** *the* *proposed* *method.* *Comparison* **of** *the* *results* *with* *some* *existing* *methods* *shows* *the* *superiority* **of** *the* *accuracy* **of** *the* *method.

摘要：

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In* *this* *paper* *we* *applicate* *the* *Hungarian* *algorithm* *for* *assignment
problem* *to* *solve* *traveling* *salesman* *problem.* *Tree* *examples* **of** *application* **of** *algorithm* *are* *included.

摘要：

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A* *quasi-exactly* *solvable* *model* *refers* *to* *any* *second* *order* *differential* *equation* *with* *polynomial* *coefficients* **of** *the* *form* *A(x)y’’(x)+B(x)y’(x)+C(x)y(x)=0
* ** *where* *a* *pair* **of** *exact* *polynomials* *{y(x),* *C(x)}* *with* *respective* *degrees* *{deg[y]=n,* *deg[C]=p}* *are* *to* *be* *found* *simultaneously* *in* *terms* **of** *the* *coefficients* **of** *two* *given* *polynomials* *{A(x),* *B(x)}.* *The* *existing* *methods* *for* *solving* *quasi-exactly* *solvable* *models* *require* *the* *solution* **of** *a* *system* **of** *nonlinear* *algebraic* *equations* **of** *which* *the* *dimensions* *depend* *on* *n,* *the* *degree* **of** *the* *exact* *polynomial* *solution* *y(x).* *In* *this* *paper,* *a* *new* *method* *employing* *a* *set* **of** *polynomials,* *called* *canonical* *polynomials,* *is* *proposed.* *This* *method* *requires* *solving* *a* *system* **of** *nonlinear* *algebraic* *equations* **of** *which* *the* *dimensions* *depend* *only* *on* **p*,* *the* *degree* **of** *C(x),* *and* *do* *not* *vary* *with* *n.* *Several* *examples* *are* *implemented* *to* *testify* *the* *efficiency* **of** *the* *proposed* *method.

摘要：

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It* *is* *well* *known* *that* *the* *full* *compressible* *Navier-Stokes* *equations* *with* *viscosity* *and* *heat* *conductivity* *coefficients* **of** *order* **of** *the* *Knudsen* *number* *ò>0* ** *can* *be* *deduced* *from* *the* *Boltzmann* *equation* *via* *the* *Chapman-Enskog* *expansion.* *In* *this* *paper,* *we* *carry* *out* *the* *rigorous* *mathematical* *study* **of** *the* *compressible* *Navier-Stokes* *equation* *with* *the* *initial-boundary* *value* *problems.* *We* *construct* *the* *existence* *and* *most* *importantly* *obtain* *the* *higher* *regularities* **of** *the* *solutions* **of** *the* *full* *compressible* *Navier-Stokes* *system* *with* *weak* *viscosity* *and* *heat* *conductivity* *in* *a* *general* *bounded* *domain.

摘要：

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In* *this* *study* *we* *discuss* *the* *use* **of** *the* *simplex* *method* *to* *solve* *allocation* *problems* *whose* *flow* *matrices* *are* *doubly* *stochastic.* *Although* *these* *problems* *can* *be* *solved* *via* *a* *0* *-* *1* *integer* *programming* *method,* *H.* *W.* *Kuhn* * href="#ref1">[1]* *suggested* *the* *use* **of** *linear* *programming* *in* *addition* *to* *the* *Hungarian* *method.* *Specifically,* *we* *use* *the* *existence* *theorem* **of** *the* *solution* *along* *with* *partially* *total* *unimodularity* *and* *nonnegativeness* **of** *the* *incidence* *matrix* *to* *prove* *that* *the* *simplex* *method* *facilitates* *solving* *these* *problems.* *We* *also* *provide* *insights* *as* *to* *how* *a* *partition* *including* *a* *particular* *unit* *may* *be* *obtained.

摘要：Introductory* *Statistics* *is* *a* *course* *taught* *in
various* *community* *colleges,* *state* *colleges,* *and* *universities.* *Implementation* **of*
projects* *in* *this* *course* *has* *been* *shown* *to* *enhance* *students'* *learning;* *in
addition* *to* *increasing* *the* *ability* **of** *educators* *to* *assess* *students'* *learning* *outcomes
in* *detail.* *These* *projects* *are* *often* *inquiry-based* *and* *require* *a* *balance* *between
flexibility* *and* *efficiency.* *Maintaining* *balance* *has* *provided* *the* *students'
opportunities* *through* *exploration* *and* *learner* *autonomy.* *In* *exploration,* *a
student* *seeks* *new* *methods* *and* *options* *through* *experimenting.* *In* *this* *paper,* *we
will* *discuss* *the* *benefits* **of** *exploration* *required* *by* *projects* *given* *in* *an
introductory* *statistics* *course.* *The* *details* **of** *five* *different* *projects
discussed* *in* *this* *paper—illustrate* *the* *practical* *influence* *that* *they* *could* *have
on* *higher* *statistics* *courses....

18.
The* *Approximated* *Semi-Lagrangian* *WENO* *Methods* *Based* *on* *Flux* *Vector* *Splitting* *for* *Hyperbolic* *Conservation* *Laws

摘要：The* *paper
is* *devised* *to* *combine* *the* *approximated* *semi-Lagrange* *weighted* *essentially
non-oscillatory* *scheme* *and* *flux* *vector* *splitting.* *The* *approximated* *finite
volume* *semi-Lagrange* *that* *is* *weighted* *essentially* *non-oscillatory* *scheme* *with
Roe* *flux* *had* *been* *proposed.* *The* *methods* *using* *Roe* *speed* *to* *construct* *the* *flux
probably* *generates* *entropy-violating* *solutions.* *More* *seriously,* *the* *methods
maybe* *perform* *numerical* *instability* *in* *two-dimensional* *cases.* *A* *robust* *and
simply* *remedy* *is* *to* *use* *a* *global* *flux* *splitting* *to* *substitute* *Roe* *flux.* *The
combination* *is* *tested* *by* *several* *numerical* *examples.* *In* *addition,* *the
comparisons* **of** *computing* *time* *and* *resolution* *between* *the* *classical* *weighted
essentially* *non-oscillatory* *scheme* *(WENOJS-LF)* *and* *the* *semi-Lagrange* *weighted
essentially* *non-oscillatory* *scheme* *(WENOEL-LF)* *which* *is* *presented* *(both
combining* *with* *the* *flux* *vector* *splitting)....

摘要：In* *this
article* *I* *conduct* *a* *short* *review* **of** *the* *proofs* **of** *the* *area* *inside* *a* *circle.
These* *include* *intuitive* *as* *well* *as* *rigorous* *analytic* *proofs.* *This* *discussion* *is
important* *not* *just* *from* *mathematical* *view* *point* *but* *also* *because* *pedagogically
the* *calculus* *books* *still* *use* *circular* *reasoning* *today* *to* *prove* *the* *area* *inside
a* *circle* *(also* *that* **of** *an* *ellipse)* *on* *this* *important* *historical* *topic,* *first
illustrated* *by* *Archimedes.* *I* *offer* *an* *innovative* *approach* *through* *the* *introduction
*of** *a* *theorem,* *which* *will* *lead* *to* *proving* *the* *area* *inside* *a* *circle* *avoiding
circular* *argumentation....

20.
Peristaltic* *Transport* **of** *Magnetohydrodynamic* *Carreau* *Nanofluid* *with* *Heat* *and* *Mass* *Transfer* *inside* *Asymmetric* *Channel

摘要：In* *this* *work,* *the* *peristaltic* *motion* **of** *a* *nano* *non-Newtonian* *fluid* *which
obeys* *Carreau* *model* *through* *a* *porous* *medium* *inside* *an* *asymmetric* *channel* *is
investigated.* *The* *hall* *current* *effects* *with* *Joule* *heating* *and* *viscous
dissipation* *are* *considered.* *The* *problem* *is* *modulated* *mathematically* *by* *a* *set* **of*
nonlinear* *partial* *differential* *equations* *which* *describe* *the* *conservation* **of*
mass,* *momentum,* *energy* *and* *concentration* **of** *nanoparticles.* *The* *non-dimensional
form* **of** *these* *equations* *is* *simplified* *under* *the* *assumption* **of** *long* *wavelength
and* *low* *Reynolds* *number,* *and* *then* *resulting* *equations* **of** *coupled* *nonlinear
differential* *equations* *are* *tackled* *numerically* *with* *appropriate* *boundary
conditions.* *Graphical* *results* *are* *presented* *for* *dimensionless* *velocity,* *temperature,
concentration* *and* *pressure* *gradient* *in* *order* *to* *illustrate* *the* *variations* **of*
various* *parameters* **of** *this* *problem* *on* *these* *obtained* *solutions....

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