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### Conditional computability of real functions with respect to a class of operators

Ivan Georgiev, Dimiter Skordev
2013 Annals of Pure and Applied Logic
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or  ...  conditionally computable with respect to this class.  ...  Uniform and conditional computability of a real function with respect to a class of operators As in  , a triple ( f, g, h) ∈ T 3 1 is called to name a real number ξ if f (t) − g(t) h(t) + 1 − ξ <  ...

### Characterization theorem for the conditionally computable real functions [article]

Ivan Georgiev
2017 arXiv   pre-print
The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains.  ...  The class of conditionally computable real functions with respect to the same class of operators is a proper extension of the class of uniformly computable real functions and it computes the elementary  ...  This is the reason to consider the second notion, which is conditional computability of real functions with respect to a class of operators.  ...

### On Some Computability Notions for Real Functions

Dimiter Skordev
2013 Computability - The Journal of the Assosiation
Thanks are due to Ivan Georgiev for helping to make certain improvements of the English and to correct several misprints (in particular, some ones in formulas).  ...  If O is the class of all computable total operators then the uniform O-computability of a real function coincides with its computability in the sense of  (naturally extended to functions of any number  ...  Definition 3 (of a computability notion for real functions) Let O be a class of total operators, N ∈ N and θ ∶ D → R, where D ⊆ R N .  ...

### The closure properties on real numbers under limits and computable operators

Xizhong Zheng
2002 Theoretical Computer Science
All these classes correspond to some kind of (weak) computability of the real numbers.  ...  Among others, we show that the class of weakly computable real numbers is not closed under e ective limit and partial computable functions while the class of recursively approximable real numbers is closed  ...  Hence a computable real function can have any type of domain, because f A is a computable function with domain A for any set A ⊆ dom( f), whenever f is computable.  ...

### Page 221 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 46, Issue 3 [page]

1940 American Mathematical Society. Bulletin of the American Mathematical Society
The problem is to investigate the manner of increase of monotone functions over an interval or over a perfect set of points and to form classes of functions with com- mon behavior in this respect.  ...  When the values of a function f(x) are to be tabulated over a fairly wide range of the argument x, it is frequently convenient to compute the function and its deriva-  ...

### Characterizing Computable Analysis with Differential Equations

Manuel L. Campagnolo, Kerry Ojakian
2008 Electronical Notes in Theoretical Computer Science
The functions of Computable Analysis are defined by enhancing the capacities of normal Turing Machines to deal with real number inputs.  ...  We combine the results of  and Graça et. al. , to show that a different function algebra also yields Computable Analysis.  ...  In this paper we propose a class of real recursive functions which is simpler in some respects, avoiding the use of a root-finding operation, which has the disadvantage of directly mimicking the operation  ...

### Real recursive functions and their hierarchy

Jerzy Mycka, José Félix Costa
2004 Journal of Complexity
In this paper, we show that a most natural operator captured from analysis-the operator of taking a limit-can be used properly to enhance the theory of recursion over the reals, providing good solutions  ...  In the last years, recursive functions over the reals (Theoret. Comput.  ...  few mistakes in a paper.  ...

### Subclasses Of Bi-Univalent Functions Associated With Hohlov Operator

Rashidah Omar, Suzeini Abdul Halim, Aini Janteng
2017 Zenodo
The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f'(0) – 1=0.  ...  In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced.  ...  Ma and Minda  positive real part is considered in the unit disk , 0 1, 0 0, and maps onto a region starlike with respect to 1 and symmetric with respect to the real axis.  ...

### Subclasses Of Bi-Univalent Functions Associated With Hohlov Operator

Rashidah Omar, Suzeini Abdul Halim, Aini Janteng
2017 Zenodo
The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f'(0) – 1=0.  ...  In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced.  ...  Ma and Minda  positive real part is considered in the unit disk , 0 1, 0 0, and maps onto a region starlike with respect to 1 and symmetric with respect to the real axis.  ...

### Continuous optimization problems and a polynomial hierarchy of real functions

Ker-I Ko
1985 Journal of Complexity
A natural extension of NP-time computable real functions to a polynomial hierarchy of real functions has a characterization by alternating operations of maximization and minimization.  ...  We examine this relationship on real functions and give a characterization of NP-time computable real functions by the maximization operation.  ...  It is natural to define Z g,c[,,, ,I, k 2 1, to be the class of real functions f on [0, l] that is computable by a polynomial-time two-oracle NTM M with respect to an oracle B E Xc--,, in the sense that  ...

### Matching class diagrams

Sabrina Uhrig
2008 Proceedings of the 2008 international workshop on Comparison and versioning of software models - CVSM '08
In this position paper we describe our ongoing work, the idea of an algorithm which works with estimated transformation costs in order to reduce the computation costs.  ...  We wonder if an exact algorithm can be designed which computes a minimal cost matching between the elements of the class diagrams and which, although it shows a non-polynomial worst case behaviour, delivers  ...  The cost function c(ai, bj) denotes the minimal editing costs of transforming the class ai into bj with respect to the feasible edit operations which have been defined in section 2.2.  ...

### Object-oriented Pseudo-spectral code TARANG for turbulence simulation [article]

Mahendra K. Verma
2011 arXiv   pre-print
We use the object-oriented features of C++ to abstract operations involved in the simulation. TARANG has been validated and used for solving problems in convection and MHD.  ...  In this paper we describe the design and implementation of TARANG, a pseudospectral code to simulate turbulent flows in fluids, magnetohydrodynamics (MHD), convection, passive scalar, etc.  ...  The indexing of the array is similar to that of CVF. Class RSF: Real Scalar Field The class RSF stands for Real Scalar Field, and it contains a dynamic array associate with a scalar.  ...

### An object-oriented approach to model management [chapter]

Vilas Wuwongse, Jian MA
1991 Lecture Notes in Computer Science
The framework consists of two major parts: a conceptual structure, within which a decision model is represented in the form of a class and an inheritance mechanism enables a new class to be specified by  ...  making use of properties in existing ones; and manipulation operations, which is a set of high-level operators for the retrieval and update operations in a model management system.  ...  They are defined as follows: FIND: to select class names or expression lists in a MMS, whenever some conditions are met: FIND target-list WHERE condition PROJECT: to form a new class with the extracts  ...

### A minimal representation for continuous functions [article]

Franz Brauße, Florian Steinberg
2018 arXiv   pre-print
This paper removes the additional premise of length-monotonicity, and instead imposes further conditions on the speed of the evaluation: The operation should now be computable in "hyper-linear" time.  ...  Ultimatively, this is due to a failure of polynomial-time computability of an upper bound to a modulus of continuity.  ...  Comparison to second-order representations This chapter presents a hardness result for an operation with respect to the representation ξC : It is impossible to compute a modulus of continuity of a function  ...

### Page 2973 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews
The effective functions (the first notion) are defined only on computable real numbers and are Type | computable with respect to a numbering of the computable real numbers.  ...  They are exactly those functions which are Type 2 computable with respect to an appropriate representation of the real numbers.  ...
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