instruction_seed stringlengths 0 115k | reasoning stringlengths 0 121k | deepseek_solution stringlengths 0 22.2k | source stringclasses 59
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Consider a scenario in which a virtual particle-antiparticle pair is produced from the vacuum near the event horizon of a black hole. Assuming the particle has negative energy and the antiparticle has positive energy, discuss the gravitational interaction between the black hole and the negative energy particle. Specifi... | Okay, let me try to work through this problem step by step. So, the question is about a virtual particle-antiparticle pair produced near a black hole's event horizon. One has negative energy, the other positive. The negative energy particle interacts gravitationally with the black hole, and we need to derive its energy... | In a scenario where a virtual particle-antiparticle pair is produced near a black hole's event horizon, the negative-energy particle interacts gravitationally with the black hole and other particles. Here's a structured analysis:
### **Energy-Momentum Tensor for the Negative Energy Particle**
The energy-momentum tenso... | facebook/natural_reasoning | [
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"from": "human",
"value": "Consider a scenario in which a virtual particle-antiparticle pair is produced from the vacuum near the event horizon of a black hole. Assuming the particle has negative energy and the antiparticle has positive energy, discuss the gravitational interaction between the black hole ... | meta_no_pipeline::select_a1_math_natural_reasoning |
What is 75600 / 350? | Alright, let me try to figure out what 75600 divided by 350 is. Okay, division... I remember that division is like splitting a number into equal parts. So here, we're splitting 75600 into 350 equal parts. Hmm, that's a big number divided by another big number. Maybe I can simplify this somehow.
First, let me write it ... | To solve \( \frac{75600}{350} \), we can simplify the division by breaking down the numbers into their prime factors and canceling common factors.
1. **Prime Factorization**:
- \( 75600 = 2^4 \times 3^3 \times 5^2 \times 7 \)
- \( 350 = 2 \times 5^2 \times 7 \)
2. **Cancel Common Factors**:
- Common factors ... | Lap1official/Math_small_corpus | [
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"value": "<think>\nAlright, let me try to figure out what 75600 divided by 350 is. Okay, division... I remember that division is like splitting a number into equal parts. So here, we're splitting 75600 into 350 equal parts. H... | meta_no_pipeline::select_a1_math_lap1official_math |
In a mysterious temple, there are 5 pressure plates, each with a different symbol etched onto it. When a plate is stepped on, it triggers a specific sound. If a combination of plates is stepped on simultaneously, the resulting sound is a unique mixture of the individual sounds. However, if the same plate is stepped on ... | Okay, so there's this temple with 5 pressure plates, each has a different symbol. When you step on a plate, it makes a specific sound. But if you step on multiple plates at the same time, the sound is a mix of the individual ones. However, if you step on the same plate multiple times in a combination, that plate's soun... | The problem involves 5 pressure plates, each producing a specific sound when stepped on. When a combination of plates is stepped on simultaneously, the resulting sound is a mixture of the individual sounds. However, if a plate is stepped on multiple times in a combination, its sound is silenced.
Key points:
1. Each pl... | ai2-adapt-dev/openmath-2-math | [
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"from": "human",
"value": "In a mysterious temple, there are 5 pressure plates, each with a different symbol etched onto it. When a plate is stepped on, it triggers a specific sound. If a combination of plates is stepped on simultaneously, the resulting sound is a unique mixture of the individual sounds. ... | meta_no_pipeline::select_a1_math_open2math |
"Finally Fox Ciel arrived in front of her castle!\n\nShe have to type a password to enter her castle(...TRUNCATED) | "Okay, let's see. The problem is about flipping panels to reach a specific state. The initial state (...TRUNCATED) | "To solve this problem, we need to determine the minimal number of operations required to flip speci(...TRUNCATED) | nvidia/OpenCodeReasoning | [{"from":"human","value":"Finally Fox Ciel arrived in front of her castle!\n\nShe have to type a pas(...TRUNCATED) | meta_no_pipeline::select_a1_code_opencodereasoning |
"Consider the concept of other universes and the argument that if they exist, the sky would be fille(...TRUNCATED) | "Okay, so I need to talk about the possibility of detecting other universes, considering things like(...TRUNCATED) | "The possibility of detecting or proving the existence of other universes hinges on fundamental prin(...TRUNCATED) | facebook/natural_reasoning | [{"from":"human","value":"Consider the concept of other universes and the argument that if they exis(...TRUNCATED) | meta_no_pipeline::select_a1_math_natural_reasoning |
"In a topological space $X$, consider a sequence of open sets $\\{K_n\\}$ such that $\\bigcup K_n = (...TRUNCATED) | "Okay, so I have this topology problem here, and I need to figure out if, given a sequence of open s(...TRUNCATED) | "Given a topological space \\(X\\), a sequence of open sets \\(\\{K_n\\}\\) such that \\(\\bigcup K_(...TRUNCATED) | zwhe99/DeepMath-103K | [{"from":"human","value":"In a topological space $X$, consider a sequence of open sets $\\{K_n\\}$ s(...TRUNCATED) | meta_no_pipeline::select_a1_math_deepmath |
"Suppose there are two players, A and B, playing a signaling game. Player A has two possible types: (...TRUNCATED) | "Okay, let's see. I need to find the probability that player A is type 1 given that player B receive(...TRUNCATED) | "To find the probability that player A is type 1 given that player B received a \"good\" signal, we (...TRUNCATED) | TIGER-Lab/MathInstruct | [{"from":"human","value":"Suppose there are two players, A and B, playing a signaling game. Player A(...TRUNCATED) | meta_no_pipeline::select_a1_math_tiger_lab_math |
"Can you modify the following Ruby formula to ensure that both Rake and RubyGems are installed by de(...TRUNCATED) | "Okay, so I need to modify this Ruby formula to make sure that Rake and RubyGems are installed by de(...TRUNCATED) | "To modify the Ruby formula to ensure Rake and RubyGems are installed by default, the code responsib(...TRUNCATED) | bigcode/commitpackft | [{"from":"human","value":"Can you modify the following Ruby formula to ensure that both Rake and Rub(...TRUNCATED) | meta_no_pipeline::select_a1_code_octopack_sft |
"A circle with radius $r$ is inscribed in a parabola $y=x^2+a^2$. How many values of $a$ satisfy tha(...TRUNCATED) | "Okay, so I need to figure out how many values of \\( a \\) satisfy the condition that a circle insc(...TRUNCATED) | "Given a circle inscribed in the parabola \\( y = x^2 + a^2 \\) and tangent to the line \\( y = a^2 (...TRUNCATED) | nvidia/OpenMathInstruct-2 | [{"from":"human","value":"A circle with radius $r$ is inscribed in a parabola $y=x^2+a^2$. How many (...TRUNCATED) | meta_no_pipeline::select_a1_math_openmathinstruct2 |
"How does cellular senescence contribute to the aging process, and what are the molecular mechanisms(...TRUNCATED) | "Okay, so I need to understand how cellular senescence contributes to aging and what molecular mecha(...TRUNCATED) | "Cellular senescence contributes to aging through two primary pathways: **loss of tissue regenerativ(...TRUNCATED) | AdapterOcean/biology_dataset_standardized_unified | [{"from":"human","value":"How does cellular senescence contribute to the aging process, and what are(...TRUNCATED) | meta_no_pipeline::select_a1_science_biology_standardized |
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