Mathematics

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  1. Can this version of the halting problem be solved?

  2. Deriving the asymptotic estimate (9.62) in Concrete Mathematics

  3. Find $\arg\min_{x \in \mathbb{R}^n} w_1\|x - a\|_1 + w_2\|x - b\|_2$

  4. Its possible integrate this with elementary calculus?
  5. Limit problem: $\lim_{t\to1} \frac {\sqrt {2t^2-1}\sqrt[3]{4t^3-3t}-1}{t^2-1}$
  6. Determining whether eigenvalues are positive, negative or 0.
  7. $f$ and $m$ are polynomials over the field $K$. Prove that if $f=pm+r$, $r≠0$, then their hcf is $1$

  8. If a function f: R-> R is monotone increasing on R and f(R) is compact, is f continuous?

  9. Homeomorphism to Cantor set and surjection onto $[0,1]$
  10. Wrong Wolfram Alpha result for $\lim_{(x,y)\to(0,0)}\frac{xy^4}{x^4+x^2+y^4}$?
  11. Is this continuity proof valid?
  12. Need help setting up and solving dual problem

  13. Equivalent Sequential Definitions of Continuity

  14. The unit ball in $L^{\infty}$ is weakly sequentially compact.

  15. Is it possible to construct eigenvalues and eigenvectors of Hamiltonian based on its subspaces?
  16. Is the space $(X,p)$ complete? If not what is its completion?

  17. $\mu,\nu$ ergodic implies $\mu\perp\nu$

  18. Integral involving the exponential and the modified BesselK function

  19. Show that $(X+Y+Z)^n = X^n + Y^n + Z^n$ if $XY = qYX$ and $YZ = q ZY$ and $ZX = qX Z$

  20. A problem on rank of a matrix over two fields
  21. $25! \pmod {78125}$
  22. How can I tell if the improper integral of $1/(1+u^8)$ converges, and how can I compute that limit?

  23. Arzela Ascoli counterexamples

  24. Solving formulas involving multiple means and standard deviations

  25. Lines that pass through a cube

  26. Indicator functions vs. conditions
  27. Intuitive meaning behind the Discriminant
  28. Question about CoCoa system and Reduced Gröbner Basis
  29. Implication vs biimplication theorems

  30. What is the largest planar clique in n-dimensions?

  31. How to find this binomial summation
  32. Number theory question from today's Pre - RMO
  33. Is the isomorphism between $\Lambda^2(\mathbb{R}^n)$ and $\mathfrak{so}(n)$ typical?
  34. Rotation around an object's center in a different coordinate system
  35. Probability of dice roll (board games)
  36. Distribution of infinite sum of Bernoulli

  37. Need help to understand the following number theory proof
  38. Write the set $G$ as the union of two disjoint nonempty separated subsets
  39. What is meant by time $y^{1 + o(1)}$?
  40. Chart for surface in $\Bbb L^4$ with positive relative nullity
  41. Finding Eigenvectors [Confused]

  42. Yoneda lemma natural isomorphism proof question
  43. Existence of a lifting for simply connected covering.
  44. Help with an Algebraic Proof that has Two Variables and a Square Root
  45. A function $f$ such that $\lim_{x\to b}f(x)=+\infty$ and $\lim_{x\to b}f'(x)=-\infty$

  46. A problem on sequence of real numbers

  47. Proof - a vertex in a path has an even number of edges Eulerian cycle
  48. Binomial limit evaluation

  49. Describe ideals in $\mathcal{L}(H)$
  50. Hilbert scheme of $n$ point action, torus action fixed points

  51. A version of KKT theorem. Looking for a reference

  52. Expectation over all ray directions
  53. How to find the maximum surface area of a torus with a fixed volume?
  54. What is the domain of convergence for $ \sum_{(a,b) \in \mathbb{Z}^2} \frac{a^4 + b^4}{(a^2 + b^2)^s} $ with $(a,b) \neq (0,0)$?

  55. Complement birthday problem with at least 4 people discrete

  56. Is $\mathbb{R}[x]/(x^2+1) \cong \mathbb{C}$?

  57. Scale invariance and $1/f^2$ power spectrum

  58. Shooting tangent to a moving circle
  59. Show $f(x)=x\sec(x)$ is one-to-one on$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

  60. Need help to plot survey distribution
  61. Residues of a function with two different essential singularities

  62. Irregular singular point & Frobenius form
  63. Does anyone know a simple proof for the fundamental theorem of finitely generated abelian group?
  64. Semigroup property heat equation
  65. Equivalence of matrices and operators
  66. Factorization of an ideal

  67. Showing that replacing functions with values preserves concavity

  68. How can I merge 2 Delaunay triangulations / Voronoï diagrams?

  69. Solve using time hierarchy

  70. linear algebra, inner product spaces.

  71. Difference between epimorphism, isomorphism, endomorphism and automorphism Linear transformations with examples

  72. proof linear transformation injective, surjective, isomorphism

  73. How many ways in total that $10$ people can enter the room?
  74. Informal Proof for tautology
  75. Which are the homomorphisms between the two groups $G=Z/(3)$ and $H=Z/(5)$?

  76. $L^1$ norm of derivative of Dirichlet kernel
  77. Singular Value Decomposition Question

  78. Calculate marginal distribution, $P(X=0|Y > 0)$, expected value and variance.

  79. Area of octagon constructed in a square

  80. Combinatorics question - Parking Cars

  81. Non-reflexive function spaces

  82. stein's complex analysis, functions of finite order.

  83. Shortest Common String Problem is NP
  84. Derivative of B-spline basis functions for degree 2

  85. Expectation of an absolute form to the power of 4.
  86. Show that $(ax^k+b)^{1/k}$ increases in function of $k$
  87. Maximizing area of a pentagon inscribed inside a circle

  88. If $\lambda$ is a weight of an irreducible $\mathbb{C}S_n$-module, and $\lambda_{i+1}=\lambda_i\pm 1$, then $\mu=s_i\lambda$ is not a weight?
  89. In how many ways can a test be passed with just $10$ right answers if at least $4$ right answers must be from part A of the test?
  90. Pi series that converges arbitrarily fast.

  91. Convergence of an improper integral $ \log( 1 + 2\operatorname{sech}x)$

  92. Certain Subset of Sorgenfrey Plane is Closed

  93. Equilibria and stability/Proving heteroclinic orbits

  94. Solving this non homogeneous IVP using power series

  95. How can we extend a base of a vector space to a base of a larger vector space?

  96. Lagrange polynom interpolation

  97. What can be said about coverings when there is no universal cover?

  98. Do there exist $2 \times 2$ matrices satisfying $XY = q YX$, $YZ = q ZY$ and $ZX = q XZ$

  99. If we assume merely that the partials $D_jf$ exist in a neighborhood of $a$ and are continuous at $a$ then $f$ is differentiable in $a$.
  100. An asymptotic formula for a nested radical