17,334 research outputs found
Retrenching the Purse: Hashing Injective CLEAR Codes, and Security Properties
No full textThe Mondex Electronic Purse is an outstanding example of industrial scale formal refinement, and was the first verification to achieve ITSEC level E6 certification. A formal abstract model and a formal concrete model were developed, and a formal refinement was hand-proved between them. Nevertheless, certain requirements issues were set beyond the scope of the formal development, or handled in an unnatural manner. The retrenchment Tower Pattern is used to address one such issue in detail: the use of a hash function rather than a total injective function when clearing the highly constrained purse logs. A retrenchment is constructed from the lowest level model to a model using a hash, and is then lifted to create two refinement developments, working at different levels of detail, and connected via retrenchments. The tower development is appropriately validated, vindicating the design used
On not open linear continuous maps between Banach spaces
No full textLet and be infinite-dimensional Banach spaces. Let be a linear continuous operator with dense range and . It is proved that, for each , there exists a quotient map , such that is an infinite-dimensional Banach space with a Schauder basis and is a nuclear operator of norm . Thereby, we obtain with respect to quotient spaces the proper analogue result of KATO concernig the existence of not trivial nuclear restrictions of not open linear continuous operators between Banach spaces. As a consequence, it is derived a result of OSTROVSKII concerning Banach spaces which are completions with repsect to total nonnorming subspaces
Convergence results for a class of pramarts and superpramarts in Banach spaces
No full textWe prove several results in the convergence of vector-valued pramarts and convex weakly compact valued pramarts-sub-superpramarts in a separable Banach space. We also establish several a.s. norm convergence of vector-valued pramarts in the dual of a separable Banach space. An unusual convergence result for bounded positive vector-valued submartingales in separable order continuous Banach lattice is provided via a renorming lattice norm and other related tools
Banach algebras and Von Neumann inequality
No full textWe propose to investigate how far Von Neumann's type inequalities extend to various classes of Banach algebras related to uniform algebras and uniform algebras. Our approach also yields estimates for the growth of norms of homogeneous polynomials in several operators on a complex Hilbert space
An Article About Albertus C. Van Raalte, Author Unknown, Except for Parts Taken from an Article by Anna C. Post
Full text linkAn article about Albertus C. Van Raalte, author unknown, except for parts taken from an article by Anna C. Post. The author knew first generation persons in the Holland settlement and therefore, the article has some value.https://digitalcommons.hope.edu/vrp_1890s/1012/thumbnail.jp
A Radon-Nikodym theorem for a pair of Banach-valued finitely additive measures
No full textOne of the most interesting problems arising in the study of finitely additive measures (f.a.m.) concerns the existence of a Radon-Nikodým derivative for a pair of f.a.m. /λ/,/m/, with /λ/<</m/. It is known that the classical Radon-Nikodým theorem fails to be true in the finitely additive case unless some further assumption is fulfilled. The first result in this direction dates back to H. B. Maynard, who investigated the case of two scalar f.a.m. defined on an algebra of sets. The scalar case as well as the vector-valued case have been studied by various authors.
In this paper, using a recent integration theory with respect to a Banach-valued finitely additive measure, we extend Maynard's result for a pair of Banach-valued f.a.m.; to do this we make use of a condition that is equivalent to that assumed by Maynard and by J. W. Hagood, but which turns out to be strictly stronger in the case here considered, as shown by means of an example
Banach envelopes of some quasi-Banach function spaces
No full textWe show that under some assumptions on the Musielak−Orlicz function generating a quasi-Banach Musielak−Orlicz function space, the Banach envelope of the weighted Cesàro−Musielak−Orlicz space generated by a certain positive sublinear operator is a weighted -space
On the Equivalence of Solutions for a Class of Stochastic Evolution Equations in a Banach Space
Full text linkAcknowledgments:
The author wishes to thank Professor Anna Chojnowska-Michalik and the
referee for many helpful suggestions and comments.We study a class of stochastic evolution equations in a Banach
space E driven by cylindrical Wiener process. Three different analytical
concepts of solutions: generalised strong, weak and mild are defined and
the conditions under which they are equivalent are given. We apply this
result to prove existence, uniqueness and continuity of weak solutions to
stochastic delay evolution equations. We also consider two examples of
these equations in non-reflexive Banach spaces: a stochastic transport
equation with delay and a stochastic delay McKendrick equation
Order-type Henstock and McShane integrals in Banach lattice setting
No full textHenstock-type integrals are studied for functions
defined in a compact metric space T endowed with a regular
σ -additive measure μ, and taking values in a Banach lattice X.
In particular, the space [0,1] with the usual Lebesgue measure is considered.
The norm- and the order-type integral are compared and
interesting results are obtained when X is an L-space
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