On Hoffman's celebrated cycling LP example
نویسندگان
چکیده
In this short note we answer two questions that naturally arise while dealing with Hoffman’s celebrated 50-years-old cycling example for the primal simplex method to solve linear programs, where an angle θ and a scaling factor ω are adjustable parameters in his example. In particular, we determine what conditions have to be imposed on ω for cycling to occur with θ = 2π/5, and what on θ with |ω| = tan(θ).
منابع مشابه
A Weighted Variant of Riemann - Liouville Fractional Integrals on R n
and Applied Analysis 3 Moreover, ∥Hωf∥Lp Rn →Lp Rn A. 1.7 Remark 1.1. Notice that the condition 1.6 implies that ω is integrable on 0, 1 since ∫1 0 ω t dt ≤ ∫1 0 t −n/pω t dt. We naturally assumeω is integrable on 0, 1 throughout this paper. Obviously, Theorem A implies the celebrated result of Hardy et al. 6, Theorem 329 , namely, for all 0 < α < 1 and 1 < p < ∞, ‖Iα‖Lp dx →Lp x−pαdx Γ ( 1 − 1...
متن کاملA Project Scheduling Method Based on Fuzzy Theory
In this paper a new method based on fuzzy theory is developed to solve the project scheduling problem under fuzzy environment. Assuming that the duration of activities are trapezoidal fuzzy numbers (TFN), in this method we compute several project characteristics such as earliest times, latest times, and, slack times in term of TFN. In this method, we introduce a new approach which we call modif...
متن کاملAn Lp-approach for the Study of Degenerate Parabolic Equations
We give regularity results for solutions of a parabolic equation in non-rectangular domains U = ∪t∈]0,1[{t} × It with It = {x : 0 < x < φ(t)}. The optimal regularity is obtained in the framework of the space Lp with p > 3/2 by considering the following cases: (1) When φ(t) = tα, α > 1/2 with a regular right-hand side belonging to a subspace of Lp(U) and under assumption p > 1 + α. We use Labbas...
متن کاملLp–BOUNDS FOR THE BEURLING–AHLFORS TRANSFORM
Let B denote the Beurling-Ahlfors transform defined on L(C), 1 < p < ∞. The celebrated conjecture of T. Iwaniec states that its L norm ‖B‖p = p∗ − 1 where p∗ = max{p, p p−1}. In this paper the new upper estimate ‖B‖p ≤ 1.575 (p − 1), 1 < p < ∞ is found.
متن کاملHypothyroidism presenting as Hoffman's syndrome.
Muscle weakness, stiffness and delayed tendon jerk relaxation are usual features of hypothyroidism while muscle hypertrophy, myoedema and wasting are occasionally seen. A 60-year-old male, who presented with proximal muscle weakness and muscle hypertrophy has been reported here. Thyroid function tests, electromyogram and muscle biopsy established the diagnosis of thyroid myopathy with Hoffman's...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computers & OR
دوره 34 شماره
صفحات -
تاریخ انتشار 2007