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47
Functional Sequence from a Domain to a Domain
, 1992
"... this paper. For simplicity, we use the following convention: D, D 1 , D 2 denote non empty sets, n, k ..."
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this paper. For simplicity, we use the following convention: D, D 1 , D 2 denote non empty sets, n, k
Trigonometric Functions and Existence of Circle Ratio
 Journal of Formalized Mathematics
, 1998
"... this article, we defined sinus and cosine as real part and imaginary part of exponential function on complex, and gave thier series expression either. Then we proved the differentiablity of sin, cos and exponential function of real. At last, we showed the existence of circle ratio, and some formulas ..."
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Cited by 13 (1 self)
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this article, we defined sinus and cosine as real part and imaginary part of exponential function on complex, and gave thier series expression either. Then we proved the differentiablity of sin, cos and exponential function of real. At last, we showed the existence of circle ratio, and some formulas of sin, cos. MML Identifier: SINCOS.
Inverse Trigonometric Functions arctan and arccot
 FORMALIZED MATHEMATICS VOL. 16, NO. 2, PAGES 147–158, 2008
, 2008
"... This article describes definitions of inverse trigonometric functions arctan, arccot and their main properties, as well as several differentiation formulas of arctan and arccot. ..."
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Cited by 7 (3 self)
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This article describes definitions of inverse trigonometric functions arctan, arccot and their main properties, as well as several differentiation formulas of arctan and arccot.
Inverse Trigonometric Functions Arcsin and Arccos
, 2005
"... Notions of inverse sine and inverse cosine have been introduced. Their basic properties have been proved. ..."
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Cited by 6 (0 self)
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Notions of inverse sine and inverse cosine have been introduced. Their basic properties have been proved.
Partial Differentiation of Real Binary Functions
"... Summary. In this article, we define two singlevariable functions SVF1 and SVF2, then discuss partial differentiation of real binary functions by dint of one variable function SVF1 and SVF2. The main properties of partial differentiation are shown [7]. ..."
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Summary. In this article, we define two singlevariable functions SVF1 and SVF2, then discuss partial differentiation of real binary functions by dint of one variable function SVF1 and SVF2. The main properties of partial differentiation are shown [7].
Definition of Integrability for Partial Functions from R to R and Integrability for Continuous Functions
"... Summary. In this article, we defined the Riemann definite integral of partial function from R to R. Then we have proved the integrability for the continuous function and differentiable function. Moreover, we have proved an elementary theorem of calculus. ..."
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Summary. In this article, we defined the Riemann definite integral of partial function from R to R. Then we have proved the integrability for the continuous function and differentiable function. Moreover, we have proved an elementary theorem of calculus.
Real Function Uniform Continuity
, 1990
"... this paper. For simplicity, we adopt the following convention: X , X 1 , Z, Z 1 denote sets, s, g, r, p, x 1 , x 2 denote real numbers, Y denotes a subset of R, and f , f 1 , f 2 denote partial functions from R to R ..."
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Cited by 3 (1 self)
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this paper. For simplicity, we adopt the following convention: X , X 1 , Z, Z 1 denote sets, s, g, r, p, x 1 , x 2 denote real numbers, Y denotes a subset of R, and f , f 1 , f 2 denote partial functions from R to R
SecondOrder Partial Differentiation of Real Binary Functions
"... Summary. In this article we define secondorder partial differentiation of real binary functions and discuss the relation of secondorder partial derivatives and partial derivatives defined in [17]. ..."
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Summary. In this article we define secondorder partial differentiation of real binary functions and discuss the relation of secondorder partial derivatives and partial derivatives defined in [17].
Monotonic and continuous real function
 Formalized Mathematics
, 1991
"... Summary. A continuation of [13] and [11]. We prove a few theorems about real functions monotonic and continuous on interval, on halfline and on the set of real numbers and continuity of the inverse function. At the beginning of the paper we show some facts about topological properties of the set of ..."
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Summary. A continuation of [13] and [11]. We prove a few theorems about real functions monotonic and continuous on interval, on halfline and on the set of real numbers and continuity of the inverse function. At the beginning of the paper we show some facts about topological properties of the set of real numbers, halflines and intervals which rather belong to [14].