Mate.polimi.it
LIST OF PUBLICATIONS
[updated: May 2013]
[1] A. Remuzzi, B.M. Brenner, V. Pata, G. Tebaldo, R. Mariano, A. Belloro & G. Remuzzi,
Three-
dimensional reconstructed glomerular capillary network: blood flow distribution and local filtration, American Journal
of Physiology
263 (1992), F562–F572
[2] A. Remuzzi, P. Ruggenenti, L. Mosconi, V. Pata, G. Viberti & G. Remuzzi,
Effect of low-dose Enalapril
on glomerular size-selectivity in human diabetic nephropathy, Journal of Nephrology
6 (1993), 36–43
[3] H. Bercovici & V. Pata,
Classical versus free domains of attractions, Mathematical Research Letters
2 (1995),
[4] V. Pata,
L´evy type characterization of stable laws for free random variables, Transactions of the American Mathe-
matical Society
347 (1995), 2457–2472
[5] H. Bercovici & V. Pata,
The law of large numbers for free identically distributed random variables, The Annals of
Probability
24 (1996), 453–465
[6] V. Pata,
Domains of partial attraction in noncommutative probability, Pacific Journal of Mathematics
176 (1996),
[7] V. Pata,
The central limit theorem for free additive convolution, Journal of Functional Analysis
140 (1996), 359–380
[8] V. Pata,
A generalized weak law of large numbers for noncommuting random variables, Indiana University Mathe-
matics Journal
45 (1996), 591–601
[9] F. Gazzola & V. Pata,
A uniform attractor for a non-autonomous generalized Navier-Stokes equation, Zeitschrift
ur Analysis und ihre Anwendungen
16 (1997), 435–449
[10] J.M. Lindsay & V. Pata,
Some weak laws of large numbers in non-commutative probability, Mathematische
Zeitschrift
226 (1997), 533–543
[11] V. Pata,
A note on strong convergence of noncommuting random variables, Bollettino della Unione Matematica
Italiana B
11 (1997), 141–159
[12] V. Pata,
A remark on the decay of strongly continuous semigroups of bounded linear operators, Rendiconti dell’Istituto
Lombardo di Scienze e Lettere A
131 (1997), 143–149
[13] C. Giorgi, A. Marzocchi & V. Pata,
Asymptotic behavior of a semilinear problem in heat conduction with
memory, Nonlinear Differential Equations and Applications
5 (1998), 333–354
[14] M. Grasselli & V. Pata,
Longtime behavior of a homogenized model in visco-elastodynamics, Discrete and Con-
tinuous Dynamical Systems
4 (1998), 339–358
[15] V. Pata,
Sulle soluzioni a crescenza lenta di equazioni differenziali ordinarie (in Italian), Rendiconti dell’Istituto
Lombardo di Scienze e Lettere A
132 (1998), 71–83
[16] V. Pata, G. Prouse & M.I. Vishik,
Traveling waves of dissipative nonautonomous hyperbolic equations in a strip,
Advances in Differential Equations
3 (1998), 249–270
[17] H. Bercovici & V. Pata,
Stable laws and domains of attraction in free probability theory, with an appendix by Ph.
Biane, Annals of Mathematics
149 (1999), 1023–1060
[18] S. Borini & V. Pata,
Uniform attractors for a strongly damped wave equation with linear memory, Asymptotic
Analysis
20 (1999), 263–277
[19] C. Giorgi, M. Grasselli & V. Pata,
Uniform attractors for a phase-field model with memory and quadratic
nonlinearity, Indiana University Mathematics Journal
48 (1999), 1395–1445
[20] V. Pata & P. Ursino,
Rearrangeable functions on the real line, Real Analysis Exchange
24 (1998/99), 677–693
[21] H. Bercovici & V. Pata,
A free analogue of Hinˇcin’s characterization of infinite divisibility, Proceedings of the
American Mathematical Society
128 (2000), 1011–1015
[22] H. Bercovici & V. Pata,
Functions of regular variation and freely stable laws, Annali di Matematica Pura ed
Applicata
178 (2000), 245–269
[23] H. Bercovici & V. Pata,
Limit laws for products of free and independent random variables, Studia Mathematica
141 (2000), 43–52
[24] A. Giarlotta, V. Pata & P. Ursino,
Combinatorial and topological aspects of measure preserving homomorphisms,
Topology Proceedings
25 (2000), 137–166
[25] C. Giorgi, A. Marzocchi & V. Pata,
Uniform attractors for a non-autonomous semilinear heat equation with
memory, Quarterly of Applied Mathematics
58 (2000), 661–683
[26] V. Pata,
Attractors for a damped wave equation on IR3
with linear memory, Mathematical Methods in the Applied
Sciences
23 (2000), 633–653
[27] V. Pata & E. Vuk,
On the exponential stability of linear thermoelasticity, Continuum Mechanics and Thermody-
namics
12 (2000), 121–130
[28] V. Pata, K.X. Zheng & A. Zucchi,
On the reflexivity of operator algebras with isometric functional calculus,
Journal of the London Mathematical Society
61 (2000), 604–616
[29] V. Pata & A. Zucchi,
Reflexivity of C0
-operators over a multiply connected region, Journal of Operator Theory
43
[30] V. Pata & A. Zucchi,
Hyperinvariant subspaces of C0
-operators over a multiply connected region, Integral Equations
and Operator Theory
36 (2000), 241–250
[31] V. Belleri & V. Pata,
Attractors for semilinear strongly damped wave equations on R3, Discrete and Continuous
Dynamical Systems
7 (2001), 719–735
[32] C. Giorgi, M. Grasselli & V. Pata,
Well-posedness and longtime behavior of the phase-field model with memory
in a history space setting, Quarterly of Applied Mathematics
59 (2001), 701–736
noz Rivera & V. Pata,
Global attractors for a semilinear hyperbolic equation in viscoelasticity,
Journal of Mathematical Analysis and Applications
260 (2001), 83–99
[34] C. Giorgi, M.G. Naso & V. Pata,
Exponential stability in linear heat conduction with memory: A semigroup
approach, Communications in Applied Analysis
5 (2001), 121–134
[35] C. Giorgi & V. Pata,
Stability of abstract linear thermoelastic systems with memory, Mathematical Models &
Methods in Applied Sciences
11 (2001), 627–644
[36] C. Giorgi & V. Pata,
Asymptotic behavior of a nonlinear hyperbolic heat equation with memory, Nonlinear Differ-
ential Equations and Applications
8 (2001), 157–171
[37] M. Grasselli & V. Pata,
Upper semicontinuous attractor for a hyperbolic phase-field model with memory, Indiana
University Mathematics Journal
50 (2001), 1281–1308
[38] M. Grasselli & V. Pata,
On the dissipativity of a hyperbolic phase-field system with memory, Nonlinear Analysis
47 (2001), 3157–3169
[39] V. Pata,
Hyperbolic limit of parabolic semilinear heat equations with fading memory, Zeitschrift f¨
ihre Anwendungen
20 (2001), 359–377
[40] V. Pata & C. Santina,
Longtime behavior of semilinear reaction-diffusion equations on the whole space, Rendiconti
del Seminario Matematico dell’Universit`
a di Padova
105 (2001), 233–251
[41] V. Pata & A. Zucchi,
Attractors for a damped hyperbolic equation with linear memory, Advances in Mathematical
Sciences and Applications
11 (2001), 505–529
[42] M. Grasselli & V. Pata,
On the longterm behaviour of a parabolic phase-field model with memory, in “Differential
equations and control theory” (S. Aizicovici and N.H. Pavel, Eds.), pp.147–157, Lecture Notes in Pure and Appl.
Math. no.225, Marcel Dekker, New York (2002)
[43] M. Grasselli & V. Pata,
Uniform attractors of nonautonomous systems with memory, in “Evolution equations,
semigroups and functional analysis” (A. Lorenzi and B. Ruf, Eds.), pp.155–178, Progr. Nonlinear Differential Equa-tions Appl. no.50, Birkh¨
[44] M. Grasselli & V. Pata,
Phase-field system with memory effects in the order parameter dynamics, in “Mathe-
matical models and methods for smart materials” (M. Fabrizio, B. Lazzari and A. Morro, Eds.), pp.155–164, Ser. onAdv. Math. Sci. Appl. no.62, World Scientific, Singapore (2002)
[45] V. Pata & A. Villani,
Some measurability and continuity properties of arbitrary real functions, Le Matematiche
57 (2002), 63–82
[46] M. Grasselli & V. Pata,
On the damped semilinear wave equation with critical exponent, Dynamical systems and
differential equations (Wilmington, NC, 2002). Discrete and Continuous Dynamical Systems (suppl.) (2003), 351–358
[47] M. Grasselli & V. Pata,
Existence of a universal attractor for a parabolic-hyperbolic phase-field system, Advances
in Mathematical Sciences and Applications
13 (2003), 443–459
[48] M. Grasselli, V. Pata & F.M. Vegni,
Longterm dynamics of a conserved phase-field system with memory,
Asymptotic Analysis
33 (2003), 261–320
[49] S. Gatti, M. Grasselli & V. Pata,
Exponential attractors for a phase-field model with memory and quadratic
nonlinearity, Indiana University Mathematics Journal
53 (2004), 719–754
[50] S. Gatti, M. Grasselli & V. Pata,
Exponential attractors for a conserved phase-field system with memory, Physica
D
189 (2004), 31–48
[51] M. Grasselli & V. Pata,
Existence of a universal attractor for a fully hyperbolic phase-field system, Journal of
Evolution Equations
4 (2004), 27–51
[52] M. Grasselli & V. Pata,
Attractor for a conserved phase-field system with hyperbolic heat conduction, Mathematical
Methods in the Applied Sciences
27 (2004), 1917–1934
[53] M. Grasselli & V. Pata,
Asymptotic behavior of a parabolic-hyperbolic system, Communications on Pure and
Applied Analysis
3 (2004), 849–881
[54] M. Grasselli, V. Pata & G. Prouse,
Longtime behavior of a viscoelastic Timoshenko beam, Discrete and Con-
tinuous Dynamical Systems
10 (2004), 337–348
[55] M. Conti & V. Pata,
Weakly dissipative semilinear equations of viscoelasticity, Communications on Pure and
Applied Analysis
4 (2005), 705–720
[56] M. Conti, V. Pata & M. Squassina,
Strongly damped wave equations on R3
with critical nonlinearities, Commu-
nications in Applied Analysis
9 (2005), 161–176
[57] M. Conti, V. Pata & M. Squassina,
Singular limit of dissipative hyperbolic equations with memory, Discrete and
Continuous Dynamical Systems (suppl.) (2005), 200–208
[58] S. Gatti, C. Giorgi & V. Pata,
Navier-Stokes limit of Jeffreys type flows, Physica D
203 (2005), 55–79
[59] S. Gatti, M. Grasselli, A. Miranville & V. Pata,
Hyperbolic relaxation of the viscous Cahn-Hilliard equation
in 3-D, Mathematical Models & Methods in Applied Sciences
15 (2005), 165–198
[60] S. Gatti, M. Grasselli, A. Miranville & V. Pata,
On the hyperbolic relaxation of the one-dimensional Cahn-
Hilliard equation, Journal of Mathematical Analysis and Applications
312 (2005), 230–247
[61] S. Gatti, M. Grasselli, A. Miranville & V. Pata,
Memory relaxation of first order evolution equations,
Nonlinearity
18 (2005), 1859–1883
[62] S. Gatti, M. Grasselli & V. Pata,
Lyapunov functionals for reaction-diffusion equations with memory, Mathe-
matical Methods in the Applied Sciences
28 (2005), 1725–1735
[63] S. Gatti, M. Grasselli, V. Pata & M. Squassina,
Robust exponential attractors for a family of nonconserved
phase-field systems with memory, Discrete and Continuous Dynamical Systems
12 (2005), 1019–1029
[64] C. Giorgi, M.G. Naso & V. Pata,
Energy decay of electromagnetic systems with memory, Mathematical Models
& Methods in Applied Sciences
15 (2005), 1489–1502
noz Rivera & V. Pata,
On the energy decay of the linear thermoelastic plate with memory,
Journal of Mathematical Analysis and Applications
309 (2005), 1–14
[66] M. Grasselli & V. Pata,
Robust exponential attractors for a phase-field system with memory, Journal of Evolution
Equations
4 (2005), 465–483
[67] M. Grasselli & V. Pata,
Attractors of phase-field systems with memory, in “Mathematical methods and models
in phase transitions” (A. Miranville, Ed.), pp.157–175, Nova Science Publishers, Inc., New York (2005)
[68] A. Miranville & V. Pata,
On the semilinear wave equation with locally distributed nonlinear damping, in “Math-
ematical approach to nonlinear phenomena; modelling, analysis and simulations”, pp.188–197, GAKUTO Internat.
Ser. Math. Sci. Appl. no.7, Gakk¯
[69] V. Pata & M. Squassina,
On the strongly damped wave equation, Communications in Mathematical Physics
253
[70] V.V. Chepyzhov, S. Gatti, M. Grasselli, A. Miranville & V. Pata,
Trajectory and global attractors for
evolution equations with memory, Applied Mathematics Letters
19 (2006), 87–96
[71] V.V. Chepyzhov, E. Mainini & V. Pata,
Stability of abstract linear semigroups arising from heat conduction with
memory, Asymptotic Analysis
50 (2006), 269–291
[72] V.V. Chepyzhov & V. Pata,
Some remarks on stability of semigroups arising from linear viscoelasticity, Asymptotic
Analysis
46 (2006), 251–273
[73] M. Conti, V. Pata & M. Squassina,
Singular limit of differential systems with memory, Indiana University
Mathematics Journal
55 (2006), 169–216
[74] S. Gatti, M. Grasselli, A. Miranville & V. Pata,
A construction of a robust family of exponential attractors,
Proceedings of the American Mathematical Society
134 (2006), 117–127
[75] S. Gatti, M. Grasselli, A. Miranville & V. Pata,
Memory relaxation of the one-dimensional Cahn-Hilliard
equation, in “Dissipative phase transitions” (P. Colli, N. Kenmochi and J. Sprekels, Eds.), pp.101–114, Ser. Adv.
Math. Appl. Sci. 71, World Sci. Publ., Hackensack, NJ (2006)
[76] S. Gatti & V. Pata,
A one-dimensional wave equation with nonlinear damping, Glasgow Mathematical Journal
48
[77] M. Grasselli & V. Pata,
A reaction-diffusion equation with memory, Discrete and Continuous Dynamical Systems
15 (2006), 1079–1088
[78] V. Pata,
Exponential stability in linear viscoelasticity, Quarterly of Applied Mathematics
64 (2006), 499–513
[79] V. Pata & S. Zelik,
A remark on the damped wave equation, Communications on Pure and Applied Analysis
5
[80] V. Pata & S. Zelik,
Global and exponential attractors for 3-D wave equations with displacement dependent damping,
Mathematical Methods in the Applied Sciences
29 (2006), 1291–1306
[81] V. Pata & S. Zelik,
Smooth attractors for strongly damped wave equations, Nonlinearity
19 (2006), 1495–1506
[82] S. D’Asero, V. Pata & P. Ursino,
On a generalized notion of differentiability, Real Analysis Exchange
32
[83] M. Conti, S. Gatti & V. Pata,
Decay rates of Volterra equations on R
N , Central European Journal of Mathematics
5 (2007), 720–732
[84] M. Grasselli, A. Miranville, V. Pata & S. Zelik,
Well-posedness and long time behavior of a parabolic-
hyperbolic phase-field system with singular potentials, Mathematische Nachrichten
280 (2007), 1475–1509
[85] A. Miranville, V. Pata & S. Zelik,
Exponential attractors for singularly perturbed damped wave equations: a
simple construction, Asymptotic Analysis
53 (2007), 1–12
[86] V. Pata & S. Zelik,
A result on the existence of global attractors for semigroups of closed operators, Communications
on Pure and Applied Analysis
6 (2007), 481–486
[87] V. Pata & S. Zelik,
Attractors and their regularity for 2-D wave equations with nonlinear damping, Advances in
Mathematical Sciences and Applications
17 (2007), 225–237
[88] V.V. Chepyzhov, V. Pata, & M.I. Vishik,
Averaging of nonautonomous damped wave equations with singularly
oscillating external forces, Journal de Math´
ees
90 (2008), 469–491
[89] M. Conti, S. Gatti & V. Pata,
Uniform decay properties of linear Volterra integro-differential equations, Mathe-
matical Models & Methods in Applied Sciences
18 (2008), 21–45
[90] F. Di Plinio & V. Pata,
Robust exponential attractors for the strongly damped wave equation with memory. I,
Russian Journal of Mathematical Physics
15 (2008), 301–315
[91] F. Di Plinio, V. Pata & S. Zelik,
On the strongly damped wave equation with memory, Indiana University
Mathematics Journal
57 (2008), 757–780
[92] S. Gatti, A. Miranville, V. Pata & S. Zelik,
Attractors for semilinear equations of viscoelasticity with very low
dissipation, Rocky Mountain Journal of Mathematics
38 (2008), 1117–1138
[93] C. Giorgi, V. Pata & E. Vuk,
On the extensible viscoelastic beam, Nonlinearity
21 (2008), 713–733
[94] M.I. Vishik, V. Pata & V.V. Chepyzhov,
Time averaging of global attractors for nonautonomous wave equations
with singularly oscillating external forces (in Russian), Doklady Akademii Nauk
422 (2008), 164–168
[95] V.V. Chepyzhov, V. Pata & M.I. Vishik,
Averaging of 2D Navier-Stokes equations with singularly oscillating
forces, Nonlinearity
22 (2009), 351–370
[96] M. Conti & V. Pata,
On the regularity of global attractors, Discrete and Continuous Dynamical Systems
25 (2009),
[97] F. Di Plinio & V. Pata,
Robust exponential attractors for the strongly damped wave equation with memory. II,
Russian Journal of Mathematical Physics
16 (2009), 61–73
[98] S. Gatti, V. Pata & S. Zelik,
A Gronwall-type lemma with parameter and dissipative estimates for PDEs, Non-
linear Analysis
70 (2009), 2337–2343
[99] C. Giorgi, M.G. Naso, V. Pata & M. Potomkin
Global attractors for the extensible thermoelastic beam system,
Journal of Differential Equations
246 (2009), 3496–3517
[100] V. Pata,
Gradient systems of closed operators, Central European Journal of Mathematics
7 (2009), 487–492
[101] V. Pata,
Stability and exponential stability in linear viscoelasticity, Milan Journal of Mathematics
77 (2009), 333–360
[102] M. Conti, S. Gatti, M. Grasselli & V. Pata,
Two-dimensional reaction-diffusion equations with memory,
Quarterly of Applied Mathematics
68 (2010), 607-643
[103] M. Conti, E.M. Marchini & V. Pata,
Semilinear wave equations of viscoelasticity in the minimal state framework,
Discrete and Continuous Dynamical Systems
27 (2010), 1535–1552
[104] M. Coti Zelati, C. Giorgi & V. Pata,
Steady states of the hinged extensible beam with external load, Mathematical
Models & Methods in Applied Sciences
20 (2010), 43–58
[105] M. Coti Zelati, V. Pata & R. Quintanilla,
Regular global attractors of type III thermoelastic extensible beams,
Chinese Annals of Mathematics - Series B
31 (2010), 619–630
[106] M. Fabrizio, C. Giorgi & V. Pata,
A new approach to equations with memory, Archive for Rational Mechanics
and Analysis
198 (2010), 189–232
[107] S. Gatti, A. Miranville, V. Pata & S. Zelik,
Continuous families of exponential attractors for singularly
perturbed equations with memory, Proceedings of the Royal Society of Edinburgh: Section A Mathematics
140A
(2010), 329–366
[108] V. Pata,
Exponential stability in linear viscoelasticity with almost flat memory kernels, Communications on Pure
and Applied Analysis
9 (2010), 721–730
[109] V. Pata & R. Quintanilla,
On the decay of solutions in nonsimple elastic solids with memory, Journal of Mathe-
matical Analysis and Applications
363 (2010), 19–28
[110] M.D. Chekroun, F. Di Plinio, N.E. Glatt-Holtz & V. Pata,
Asymptotics of the Coleman-Gurtin model,
Discrete and Continuous Dynamical Systems - Series S
4 (2011), 351–369
[111] F. Dell’Oro & V. Pata,
Long-term analysis of strongly damped nonlinear wave equations, Nonlinearity
24 (2011),
[112] E. Laeng & V. Pata,
A convergence-divergence test for series of nonnegative terms, Expositiones Mathematicae
29 (2011), 420–424
[113] V. Pata,
Uniform estimates of Gronwall type, Journal of Mathematical Analysis and Applications
373 (2011),
[114] V. Pata,
A fixed point theorem in metric spaces, Journal of Fixed Point Theory and Applications
10 (2011), 299–305
[115] V.V. Chepyzhov, M. Conti & V. Pata,
A minimal approach to the theory of global attractors, Discrete and
Continuous Dynamical Systems
32 (2012), 2079–2088
[116] M. Conti, E.M. Marchini & V. Pata,
Approximating infinite delay with finite delay, Communications in Con-
temporary Mathematics
14 (2012), no.1250012
[117] F. Dell’Oro & V. Pata,
Strongly damped wave equations with critical nonlinearities, Nonlinear Analysis
75 (2012),
[118] F. Dell’Oro & V. Pata,
Memory relaxation of type III thermoelastic extensible beams and Berger plates, Evolution
Equations and Control Theory
1 (2012), 251–270
[119] V. Pata,
On the regularity of solutions to the Navier-Stokes equations, Communications on Pure and Applied Analysis
11 (2012), 747–761
[120] M. Conti, E.M. Marchini & V. Pata,
Exponential stability for a class of linear hyperbolic equations with hereditary
memory, Discrete and Continuous Dynamical Systems - Series B
18 (2013), 1555–1565
[121] M. Coti Zelati, F. Dell’Oro & V. Pata,
Energy decay of type III linear thermoelastic plates with memory,
Journal of Mathematical Analysis and Applications
401 (2013), 357–366
[122] V.V. Chepyzhov, M. Conti & V. Pata,
Totally dissipative dynamical processes and their uniform global attractors,
Communications on Pure and Applied Analysis
[123] M. Conti, E.M. Marchini & V. Pata,
Reaction-diffusion with memory in the minimal state framework, Transac-
tions of the American Mathematical Society
[124] M. Conti, V. Pata & R. Temam,
Attractors for processes on time-dependent spaces. Applications to wave equations,
[125] C. Giorgi, D. Grandi & V. Pata,
On the Green-Naghdi type III heat conduction model, Discrete and Continuous
Preprints
[126] M. Conti, F. Dell’Oro & V. Pata,
Timoshenko systems with fading memory[127] M. Conti, E.M. Marchini & V. Pata,
Nonclassical diffusion with memory[128] M. Conti & V. Pata,
Asymptotic structure of the attractor for processes on time-dependent spaces[129] F. Dell’Oro, J.E. Mu˜
noz Rivera & V. Pata,
Exponential and polynomial stability of linear thermoelastic plates
[130] F. Dell’Oro & V. Pata,
On the stability of Timoshenko systems with Gurtin-Pipkin thermal law
Source: http://www.mate.polimi.it/viste/pagina_personale/pp/121/Lavori.pdf
The emergency it represents in the clinical setting of : Hypertension Author : - Dr. Edward Tsang (registered Chinese Herbalist & Acupuncturist ) Wu Zhu Metaphysician Hypertension is quite common and popular for modern society nowadays due to people’s daily diet. Patients with the symptom of diastolic blood pressure over 120 mmHg is defined as hypertensive crisis (Cameron et al
DEFINITIONS Concentration of lipid in the blood of a fasted (>12 h) patient that exceeds the upper range of normal for that species; includes both hypercholesterolemia and hypertriglyceridemia Lipemic serum or plasma separated from blood that contains an excess concentration of Lactescence opaque, milklike appearance of serum or plasma that contains an even higher concentrat