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 Enalaprilon 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 withmemory, 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 quadraticnonlinearity, 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 withmemory, 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 memoryin 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 semigroupapproach, 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 quadraticnonlinearity, 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 nonconservedphase-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 forevolution 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 withmemory, 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-Hilliardequation, 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 RN , 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: asimple 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 singularlyoscillating 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 lowdissipation, 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 oscillatingforces, 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 singularlyperturbed 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 hereditarymemory, 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

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