adaptive boundary concentration control using zakai equation a mean variance control problem is formulated with respect to a partially observed nonlinear system that includes unknown constant parameters a physical prototype of the system is the cathode surface reaction in an electrolysis cell where the controller aim is to keep the boundary concentration of species in the near vicinity of the cathode surface low but not zero the boundary concentration is a diffusion controlled process observed through the measured current density and in practice controlled through the applied voltage the former incomplete data control problem is converted to complete data to the so called separated control problem whose solution is given by the infinite dimensional zakai equation in this article the separated control problem is solved numerically using pathwise integration of the zakai equation this article demonstrates precise tracking of the target trajectory with a rapid convergence of estimates to unknown parameters which take place simultaneously with control

stochastic uncertain systems subject to relative entropy constraints induced norms and monotonicity properties of minimax games entropy and relative entropy are fundamental concepts on which information theory is founded on and in general telecommunication systems design on the other hand dissipation inequalities minimax strategies and induced norms are the basic concepts on which robustness of uncertain control and estimation of systems are founded on in this paper the precise relation between these notions is investigated in particular it will be shown that the higher the dissipation the higher the entropy of the system which has implications in computing the induced norm associated with robustness these connections are obtained by considering stochastic optimal uncertain control systems in which uncertainty is described by a relative entropy constraint between the nominal and uncertain measures while the pay off is a linear functional of the uncertain measure this is a minimax game in which the controller measure seeks to minimize the pay off while the disturbance measure aims at maximizing the pay off salient properties of the minimax solution are derived including a characterization of the optimal sensitivity reduction computation of the induced norm monotonicity properties of minimax solution and relations between dissipation and relative entropy of the system the theory is developed in an abstract setting and then applied to nonlinear partially observable continuous time uncertain controlled systems in which the nominal and uncertain systems are described by conditional distributions in addition existence of the optimal control policy among the class of policies known as wide sense control laws is shown and an explicit formulae for the worst case conditional measure is derived the results are applied to linear quadratic gaussian problems

geometry of fermat adeles if l a s n c n a n s is a family of geometric l functions depending on a parameter a then the function p a c p a where p runs through the set of prime integers is not a rational function and hence is not a function belonging to algebraic geometry the aim of the paper is to show that if one enlarges algebraic geometry by adjoining a fermat quotient operation then the functions c p a become functions in the enlarged geometry at least for l functions of curves and abelian varieties

partial information state based optimization of partially observable markov decision processes and the separation principle we propose a partial information state based approach to the optimization of the long run average performance in a partially observable markov decision process pomdp in this approach the information history is summarized at least partially by a or a few statistic s not necessary sufficient called a partial information state and actions depend on the partial information state rather than system states we first propose the single policy based comparison principle under which we derive an hjb type of optimality equation and policy iteration for the optimal policy in the partial information state based policy space we then introduce the q sufficient statistics and show that if the partial information state is q sufficient then the optimal policy in the partial information state based policy space is optimal in the space of all feasible information state based policies we show that with some further conditions the well known separation principle holds the results are obtained by applying the direct comparison based approach initially developed for discrete event dynamic systems

optimal control for partially observed diffusions stochastic control problems are considered in which a state process x t and an observation process y t are governed by ito sense stochastic differential equations driven by independent brownian motions the control u t enters linearly in the dynamics of x t a separated control problem is introduced in which the state at any time t is a measure lambda t representing an unnormalized conditional distribution for x t given y s u s for s leqq t the method depends on introducing a pathwise version of lambda t which depends continuously on observation and control trajectories y u existence of an optimal control is obtained in a suitable class larger than the usual class of controls admissible in the strict sense that u t is measurable on the sigma algebra mathcal f t y generated by observations y s s leqq t the dynamics of lambda t are studied using a method of forward and backward partial differential equations under a suitable nondegeneracy condition the m

arithmetic differential equations on gln i differential cocycles abstract the theory of differential equations has an arithmetic analogue 8 in which derivatives are replaced by fermat quotients one can then ask what is the arithmetic analogue of a linear differential equation the study of usual linear differential equations is the same as the study of the differential cocycle from gl n into its lie algebra given by the logarithmic derivative 14 equivalently by the maurer cartan connection 17 however we prove here that there are no such cocycles in the context of arithmetic differential equations in sequels of this paper 10 11 we will remedy the situation by introducing arithmetic analogues of lie algebras and a skew version of differential cocycles this will lead to a theory of linear arithmetic differential equations

near optimal controller for nonlinear continuous time systems with unknown dynamics using policy iteration this paper presents a single network adaptive critic based controller for continuous time systems with unknown dynamics in a policy iteration pi framework it is assumed that the unknown dynamics can be estimated using the takagi sugeno kang fuzzy model with arbitrary precision the successful implementation of a pi scheme depends on the effective learning of critic network parameters network parameters must stabilize the system in each iteration in addition to approximating the critic and the cost it is found that the critic updates according to the hamilton jacobi bellman formulation sometimes lead to the instability of the closed loop systems in the proposed work a novel critic network parameter update scheme is adopted which not only approximates the critic at current iteration but also provides feasible solutions that keep the policy stable in the next step of training by combining a lyapunov based linear matrix inequalities approach with pi the critic modeling technique presented here is the first of its kind to address this issue though multiple literature exists discussing the convergence of pi however to the best of our knowledge there exists no literature which focuses on the effect of critic network parameters on the convergence computational complexity in the proposed algorithm is reduced to the order of f z n 1 where n is the fuzzy state dimensionality and f z is the number of fuzzy zones in the states space a genetic algorithm toolbox of matlab is used for searching stable parameters while minimizing the training error the proposed algorithm also provides a way to solve for the initial stable control policy in the pi scheme the algorithm is validated through real time experiment on a commercial robotic manipulator results show that the algorithm successfully finds stable critic network parameters in real time for a highly nonlinear system

a note on manin s theorem of the kernel the purpose of this note is to show that manin s original statement of the theorem of the kernel is an easy consequence of deligne s theory of differential equations with regular singularities and deligne s hodge theory since this note is primarily of historical interest some discussion about the history may be beneficial to the reader and i stand to be corrected for any inaccuracy more than a quarter of a century ago manin in m proved mordell s conjecture for function fields over c his major tool was what is now commonly called the gauss manin connection introduced by manin a major step is a statement called the theorem of the kernel an equivalent form of which will be recalled later recently robert coleman found a mistake in elementary linear algebra in the proof of the theorem of kernel in m which unfortunately invalidated the whole proof coleman however proved a weaker version of the theorem of kernel and deduced mordell s conjecture over function fields following manin s original ideas and he used analogue of siegel s theorem on integral points over function fields over c in this note it will be shown that manin was right after all and it is possible to make a local correction using deligne s theorems it may be of interest to note that our proof uses global monodromy of the gauss manin connection systematically instead of the local monodromy as in m i learned of manin s beautiful ideas from lectures of professor coleman on jan 7 8 1989 at the tucson conference on the arithmetic of curves this note is a response to the stimulating question he raised at tucson and i thank him very much i would also like to thank carlos simpson for pleasant discussions and a pertinent remark i strongly recommend manin s original paper m for readers interested in manin s circle of ideas about mordel s conjecture for function fields over c for a modern treatment of manin s proof using algebraic derham cohomology the reader is referred to c

new explicit filters and smoothers for diffusions with nonlinear drift and measurements the optimal least squares filtering of a diffusion x t from its noisy measurements y 0 t is given by the conditional mean e x t y 0 t when x t satisfies the stochastic diffusion equation dx t f x t dt dw t and y t 0tx s ds b t where f is a global solution of the riccati equation xf x f x 2 f x 2 x2 x for some r3 and w b are independent brownian motions benes gave an explicit formula for computing the conditional mean this paper extends benes results to measurements y t 0tx s ds 0t dx s b t and its multidimensional version without imposing additional conditions on f analogous results are also derived for the optimal least squares smoothed estimate e x s y 0 t s t the methodology relies on girsanov s measure transformations gauge transformations function space integrations lie algebras and the duncan mortensen zakai equation

array approach to fuzzy logic abstract promising results from applying an array based approach to two valued logic suggests its application to fuzzy logic the idea is to limit the domain of truth values to a discrete finite domain such that a logical relationship can be evaluated by an exhaustive test of all possible combinations of truth values the paper presents a study of the topic from an engineer s viewpoint as an example 31 logical sentences valid in two valued logic were tested in three valued logic using the nested interactive array language nial out of these 24 turned out to be valid in a three valued extension based on the well known s implication operator also called godel s implication operator applications to automated approximate reasoning and fuzzy control are also illustrated

generation of conditional densities in nonlinear filtering for infinite dimensional systems consider a signal process that takes values in an infinite dimensional space and assume that this process is observed through a nonlinear diffusion process in the nonlinear filtering theory literature recursive expressions for such problems in the form of conditional expectations and consequently measure valued stochastic partial differential equations on the underlying infinite dimensional space are obtained in this work state estimation problems for such stochastic systems are considered and nonlinear filtering equations in the form of conditional densities are obtained this is achieved by first deriving the filtering equations in the form of conditional expectations for a banach space valued state process whose dynamics depends on a finite dimensional brownian motion next a recursion for the conditional density which we assume to exist with respect to a sigma finite measure is obtained for such an analysis we obtain the adjoint operator for the generator of the state process which requires to use the theory of integration by parts in the infinite dimensional domains finally we discuss some potential application of the derived filtering equations in a portfolio optimization problem for portfolios which consist of bonds whose price curve is interpreted as a stochastic partial differential equation taking values in a banach space applications in mean field games are also demonstrated

on the relation of zakai s and mortensen s equations the problem of optimal control for partially observable diffusion processes is studied by the dynamic programming in function space approach first proposed by r e mortensen the density of the conditional distribution of the unobservable signal given past and present observations which satisfies the zakai equation of nonlinear filtering is viewed as the new state of the system a verification result is established for the corresponding bellman hamilton jacobi equation known as mortensen s equation

certain nonlinear partially observable stochastic optimal control problems with explicit control laws equivalent to leqg lqg problems this paper is concerned with partially observed stochastic optimal control problems when nonlinearities enter the dynamics of the unobservable state and the observations as gradients of potential functions explicit representations for the information state are derived in terms of a finite number of sufficient statistics consequently the partially observed problem is recast as one of complete information with a new state generated by a modified version of the kalman filter when the terminal cost is quadratic in the unobservable state and includes the integral of the nonlinearities the optimal control laws are explicitly computed similar to linear exponential quadratic gaussian leqg and linear quadratic gaussian lqg tracking problems the results are applicable to filtering and control of hamiltonian systems

torsion points on curves and p adic abelian integrals theorem a let f c j be an albanese morphism defined over a number field k of a s mooth curve of genus g into its jacobian suppose j has potential complex multiplication let s denote the set of primes p of k satisfying i p does not divide 2 or 3 ii k q is unramified at p iii c has good ordinary reduction over k then the set t of torsion points of a defined over an algebraic closure of k which lie on the image of c is defined over an extension of k unramified above s moreover to pg

the influence of some fuzzy implication operators on the accuracy of a fuzzy model part ii abstract the influence of fuzzy implication operators and the connective also on the accuracy of a fuzzy model of a d c series motor is considered some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d c series motor a root mean square error is used as the criterion of the fuzzy model s adequacy to the real system a number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model s applicability if estimated from the point of view of computing techniques the best types of fuzzy relations representing fuzzy models of a real system are chosen in order to secure the least root mean square error with minimal number of mathematical operations necessary for computer implementation

event based optimization of markov systems recent research indicates that markov decision processes mdps and perturbation analysis pa based optimization can be derived easily from two fundamental performance sensitivity formulas with this sensitivity point of view an event based optimization approach including event based sensitivity analysis and event based policy iteration was proposed via an example by x r cao discrete event dyn syst theory appl vol 15 pp 169 197 2005 this approach utilizes the special feature of a system and illustrates how the potentials can be aggregated using the special feature the approach applies to many practical problems that do not fit well the standard mdp formulation this note provides a mathematical formulation and proves the main results for this approach

optimization of average rewards of time nonhomogeneous markov chains we study the optimization of average rewards of discrete time nonhomogeneous markov chains in which the state spaces transition probabilities and reward functions depend on time the analysis encounters a few major difficulties 1 notions crucial to homogeneous markov chains such as ergodicity stationarity periodicity and connectivity no longer apply 2 the average reward criterion is under selective i e it does not depend on the decisions in any finite period and thus dynamic programming is not amenable and 3 because of the under selectivity an optimal average reward policy may not be the best in any finite period

nonlinear filtering theory for mckean vlasov type stochastic differential equations we consider estimation theory for partially observed stochastic dynamical systems whose state equations are given by mckean vlasov type stochastic differential equations and hence contain a measure term corresponding to the distribution of the solution of the state process nonlinear filtering equations are derived in this framework based upon the classification that the measure term is either stochastic or deterministic and that either the state or the measure term is estimated when the measure term is deterministic the standard theory holds further when the measure is random the induced functions in the dynamics of the state become random and a similar recursion for the optimal filter is obtained the joint estimation of state and the measure term is next considered the extended state in this setup is shown to be a banach space valued stochastic process with random functions in its state dynamics and a nonlinear filtering equation for this setup is provided the first step of such an analysis requ

total p differentials on schemes over z p2 abstract for a scheme x defined over the length 2 p typical witt vectors w 2 k of a characteristic p field we introduce total p differentials which interpolate between frobenius twisted differentials and buium s p differentials they form a sheaf over the reduction x 0 and behave as if they were the sheaf of differentials of x over a deeper base below w 2 k this allows us to construct the analogues of gauss manin connections and kodaira spencer classes as in the katz oda formalism we make connections to frobenius lifts borger weiland s biring formalism and deligne illusie classes

classes of nonlinear partially observable stochastic optimal control problems with explicit optimal control laws this paper introduces certain nonlinear partially observable stochastic optimal control problems which are equivalent to completely observable control problems with finite dimensional state space in some cases the optimal control laws are analogous to linear exponential quadratic gaussian and linear quadratic gaussian tracking problems the problems discussed allow nonlinearities to enter the unobservable dynamics as gradients of potential functions the methodology is based on explicit solutions of a modified duncan mortensen zakai equation

state classification of time nonhomogeneous markov chains and average reward optimization of multi chains in a discrete time nonhomogeneous markov chain tnhmc the states spaces transition probabilities and reward functions at different times may be different in this paper with the confluencity previously introduced we show that the states of a tnhmc can be classified into the branching states and a number of classes of confluent states versus the transient and recurrent states in the time homogeneous case the optimization of average reward in tnhmc s consisting of a single confluent class uni chain have been addressed in a previous paper by the author in this paper we show that with confluencity and the state classification and under some bound conditions we can obtain the necessary and sufficient conditions for optimal policies of the average reward of tnhmcs consisting of multiple confluent classes multi chains just like in the uni chain tnhmc case the sufficient condition does not need to hold in any zero frequently visited time sequence this under selectivity makes the problem not amenable to dynamic programming a direct comparison based approach is used to prove the results the results enhance our understanding of state classification and performance optimization with the notion of confluencity

connectives and quantifiers in fuzzy sets abstract we discuss some of the issues involved in the selection of appropriate operators for implementing the union and intersection of fuzzy subsets we discuss the extension principles used in extending operators to fuzzy subsets we provide a structure for aggregating linguistic variables in the theory of approximate reasoning we look at mean operators on fuzzy subsets as well as the inclusion of importances in aggregation we discuss non monotone set operators we introduce the concept of linguistic quantifiers and look at some applications of these structures we are particularly concerned with their application to linguistic summarizers syllogistic reasoning and multi criteria decision making

optimality conditions for long run average rewards with underselectivity and nonsmooth features we study three existing issues associated with optimization of long run average rewards of time nonhomogeneous markov processes in continuous time with continuous state spaces 1 the underselectivity i e the optimal policies do not depend on their actions in any finite time period 2 its related issue the bias optimality i e policies that optimize both long run average and transient total rewards and 3 the effects of a nonsmooth point of a value function on performance optimization these issues require considerations of the performance in the entire period with an infinite horizon and therefore are not easily solvable by dynamic programming which works backwards in time and takes a local view at a particular time instant in this paper we take a different approach called the relative optimization theory which is based on a direct comparison of the performance measures of any two policies we derive tight necessary and sufficient optimality conditions that take the underselectivity into consideration we derive bias optimality conditions for both long run average and transient rewards and we show that the effect of a wide class of nonsmooth points called semismooth points of a value function on the long run average performance is zero and can be ignored

isocrystals associated to arithmetic jet spaces of abelian schemes abstract using buium s theory of arithmetic differential characters we construct a filtered f isocrystal h a k associated to an abelian scheme a over a p adically complete discrete valuation ring with perfect residue field as a filtered vector space h a k admits a natural map to the usual de rham cohomology of a but the frobenius operator comes from arithmetic differential theory and is not the same as the usual crystalline one when a is an elliptic curve we show that h a k has a natural integral model h a which implies an integral refinement of a result of buium s on arithmetic differential characters the weak admissibility of h a k depends on the invertibility of an arithmetic differential modular parameter thus the fontaine functor associates to suitably generic a a local galois representation of an apparently new kind

the role of information state and adjoint in relating nonlinear output feedback risk sensitive control and dynamic games this paper employs logarithmic transformations to establish relations between continuous time nonlinear partially observable risk sensitive control problems and analogous output feedback dynamic games the first logarithmic transformation is introduced to relate the stochastic information state to a deterministic information state the second logarithmic transformation is applied to the risk sensitive cost function using the laplace varadhan lemma in the small noise limit this cost function is shown to be logarithmically equivalent to the cost function of an analogous dynamic game

optimal control of partially observable stochastic systems with an exponential of integral performance index the stochastic control problem with linear stochastic differential equations driven by brownian motion processes and as cost functional the exponential of a quadratic form is considered the soluti

policy iteration based feedback control it is well known that stochastic control systems can be viewed as markov decision processes mdps with continuous state spaces in this paper we propose to apply the policy iteration approach in mdps to the optimal control problem of stochastic systems we first provide an optimality equation based on performance potentials and develop a policy iteration procedure then we apply policy iteration to the jump linear quadratic problem and obtain the coupled riccati equations for their optimal solutions the approach is applicable to linear as well as nonlinear systems and can be implemented on line on real world systems without identifying all the system structure and parameters

mean variance portfolio selection under partial information this paper is concerned with a continuous time mean variance portfolio selection problem in a possibly incomplete market with multiple stocks and a bond only the past price movements of the stocks and the bond are the information available to the investors a separation principle is shown to hold in this setting efficient strategies based on the aforementioned partial information are derived which involve the optimal filter of the stock appreciation rate processes the main methodological contribution of the paper is to employ the particle system representation to develop analytical and numerical approaches in obtaining the filter as well as solving the related backward stochastic differential equation

the complexity of markov decision processes we investigate the complexity of the classical problem of optimal policy computation in markov decision processes all three variants of the problem finite horizon infinite horizon discounted and infinite horizon average cost were known to be solvable in polynomial time by dynamic programming finite horizon problems linear programming or successive approximation techniques infinite horizon we show that they are complete for p and therefore most likely cannot be solved by highly parallel algorithms we also show that in contrast the deterministic cases of all three problems can be solved very fast in parallel the version with partially observed states is shown to be pspace complete and thus even less likely to be solved in polynomial time than the np complete problems in fact we show that most likely it is not possible to have an efficient on line implementation involving polynomial time on line computations and memory of an optimal policy even if an arbitrary amount of precomputation is allowed finally the variant of the problem in which there are no observations is shown to be np complete

conditional densities for continuous time nonlinear hybrid systems with applications to fault detection continuous time nonlinear stochastic differential state and measurement equations all of which have coefficients capable of abrupt changes at a random time are considered finite state jump markov chains are used to model the changes conditional probability densities which are essential in obtaining filtered estimates for these hybrid systems are then derived they are governed by a coupled system of stochastic partial differential equations when the q matrix of the markov chain is either lower or upper diagonal it is shown that the system of conditional density equations is finite dimensional computable these findings are then applied to a fault detection problem to compute state estimates that include the failure time

geometry of differential polynomial functions ii algebraic curves introduction the present paper is a direct continuation of b5 we shall freely borrow terminology and notations from that paper which shall be referred to from now on as part i however understanding the introduction of the present paper only requires familiarity with the introduction and first appendix of part i here we investigate 6 polynomial functions of smooth projective curves x defined over a 6 closed field f we will prove the surprising result that any smooth projective curve of genus 2 over f which does not descend to c can be naturally embedded via a 6 regular map as a 6 closed subset of a projective space which lies completely outside a unique hyperplane this provides in particular remarkable new examples of ritt s anomaly on the 6 dimension of intersections r p 133 we will also prove an infinitesimal analogue of serge lang s conjecture la which in special significant cases implies our 6 algebraic analogue of lang s conjecture b4 and hence the geometric analogue of lang s conjecture let f be as in the introduction of part i a 6 closed field with derivation operator 6 and constant field c and let x be a smooth projective f variety then one can always define two sequences of 6 regular maps

solutions to arithmetic differential equations in algebraically closed fields abstract arithmetic differential equations or geometry exploits analogies between derivations and p derivations arising from lifts of frobenius to study problems in arithmetic geometry along the way two main classes such functions describable as series arose prominently namely characters of abelian schemes and isogeny covariant modular forms however the theory of these functions is not as straightforward in ramified settings overconvergence was introduced in 13 to account for these issues which essentially imposes growth conditions extensions of these series to a fixed level of ramification necessary as such extensions have non trivial fractional coefficients in this article we introduce a rescaling process which identifies a class of functions we call totally overconvergent which extend all the way to the algebraic closure of ring of integers of the maximally unramified extension of q p applications built on these functions allow one to remove boundedness assumptions on ramification the bulk of the article is devoted to establishing that most functions arising in practice namely those in the applications described in 5 7 8 are totally overconvergent which essentially extends results in 13 to unbounded ramification

optimal control of linear systems with parameter uncertainty a class of infinite horizon regulator problems is formulated for families of time invariant linear systems with parameter uncertainty under a regularity assumption the optimal linear state feedback control is shown to exist and is defined via a positive definite solution of a family of riccati type algebraic equations the solvability of these equations is equivalent to the stabilizability of the family of linear systems by a constant linear feedback

hamilton jacobi bellman equations for the optimal control of the duncan mortensen zakai equation abstract we study a class of hamilton jacobi bellman hjb equations associated to stochastic optimal control of the duncan mortensen zakai equation the equations are investigated in weighted l 2 spaces we introduce an appropriate notion of weak viscosity solution of such equations and prove that the value function is the unique solution of the hjb equation we apply the results to stochastic optimal control problems with partial observation and correlated noise

a stochastic model for electrodeposition process with applications in filtering and boundary control electrodeposition is a complex partially observed mass transfer process driven by several surface reactions without exact model in this article the process uncertainties are described by a finite number of wiener processes in a stochastic model applied in the filtering and control problems these problems are solved as a boundary observation control problem based on a finite diffusion model with uncertainties in the domain interior and on the boundaries a mixed boundary problem is considered on an interval with the dirichlet data on one end bulk solution and neumann data on the other end cathode surface the concentration of oxidising species in the domain interior is unattainable for observations but the flux on the boundary electric current can be measured with a limited accuracy sensor error the total flux for the main and side reactions is controlled by the current density on the cathode surface the disturbing effect of the side reactions is modelled as a noise the concentration of speci

information states in stochastic control and filtering a lie algebraic theoretic approach the purpose of the paper is two fold i to introduce the sufficient statistic algebra which is responsible for propagating the sufficient statistics or information state in the optimal control of stochastic systems and ii to apply certain lie algebraic methods and gauge transformations widely used in nonlinear control theory and quantum physics to derive new results concerning finite dimensional controllers this enhances our understanding of the role played by the sufficient statistics the sufficient statistic algebra enables us to determine a priori whether there exist finite dimensional controllers it also enables us to classify all finite dimensional controllers relations to minimax dynamic games are delineated

applicability of some fuzzy implication operators this paper examines the maximal errors of seventy two implication operators with various membership functions in several typical cases and shows five operators which have very good performance in fuzzy inference

arithmetic partial differential equations ii abstract we continue the study of arithmetic partial differential equations initiated in 7 by classifying arithmetic convection equations on modular curves and by describing their space of solutions certain of these solutions involve the fourier expansions of the eisenstein modular forms of weight 4 and 6 while others involve the serre tate expansions mori 1995 13 buium 2003 4 of the same modular forms in this sense our arithmetic convection equations can be seen as unifying the two types of expansions the theory can be generalized to one of arithmetic heat equations on modular curves but we prove that they do not carry arithmetic wave equations finally we prove an instability result for families of arithmetic heat equations converging to an arithmetic convection equation

differential subgroups of simple algebraic groups over p adic fields a theorem of cassidy states that any zariski closed differential algebraic subgroup of a simple linear algebraic group defined over a differential field is either the whole group or is conjugate to the subgroup of constant matrices an arithmetic analogue of this theorem is proved in which usual derivations on fields are replaced by certain nonlinear operators on p adic rings called p derivations