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In General Relativity and Quantum Gravity, diffeomorphism often called diffeomorphism invariance or general covariance is an isomorphism of differentiable manifolds that defines the physical nature of spacetime. Rather than a mathematical tool, diffeomorphism is a smooth, bijective (invertible) mapping between two open sets where both the function and its...

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Jensen's inequality gives the difference between the average value of a convex function φ, and its value at the center, where both “average” and “center” are defined in terms of some distribution p_X. When the function φ is flat, or the distribution is narrow, they agree.
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Jensen's inequality gives the difference between the average value of a convex function φ, and its value at the center, where both “average” and “center” are defined in terms of some distribution p_X. When the function φ is flat, or the distribution is narrow, they agree.

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As a gynecologist, one of the most frequently asked questions is about the ''hymen''. The hymen is not a structure located deep inside the vagina. It is a thin, flexible fold of tissue situated very close to the vaginal opening, anatomically at the entrance of the vaginal canal. It is typically found about 1–2 cm inside the vaginal opening, but in many women, it is almost at the surface. Therefore, the common belief that it is located deep inside is incorrect. One of the most important points is this: The hymen is not a closed membrane. It naturally has openings that allow menstrual blood to pass. Additionally, the structure of the hymen varies from person to person. Its thickness, elasticity, and shape are not standard. In some women, it may be very thin and elastic, while in others, it may be minimal or barely noticeable. This is completely a normal anatomical variation. A common misconception is that changes in the hymen occur only due to sexual intercourse. In reality, factors such as certain physical activities or tampon use can also lead to stretching or changes in this tissue. Therefore, the hymen is not a reliable indicator of a person’s sexual history or “virginity.” In summary, the hymen is a small and variable anatomical structure. The meanings attributed to it are largely shaped by sociocultural beliefs rather than medical facts.

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In psychoanalysis, a Freudian slip, also called parapraxis, is an error in speech, memory, or physical action that occurs due to the interference of an unconscious subdued wish or internal train of thought.

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It's been 9 days. Our children are without food, water, or medicine. People in Gaza are suffering without medicine. Where is the freedom you expressed? Where are the words of the President of Ukraine? Where are the words of the President of France? #OpenRafahCrossing
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It's been 9 days. Our children are without food, water, or medicine. People in Gaza are suffering without medicine. Where is the freedom you expressed? Where are the words of the President of Ukraine? Where are the words of the President of France? #OpenRafahCrossing

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QUOTE 1: A worldview without feelings is a cold structure; feelings without a worldview are a blind force. : The author offers a precise and balanced insight into the relationship between intellect and emotion. A worldview without feelings becomes a cold, lifeless structure rational but empty, capable of logic yet devoid of warmth or motivation. Conversely, feelings without a coherent worldview become a blind force powerful but directionless, easily manipulated or destructive. True human maturity requires the harmonious union of both. The mind provides clarity, structure, and long-term vision. Feelings supply energy, empathy, and moral intuition. When integrated, they create a living philosophy: thought that is compassionate and emotion that is wise. This synthesis is the foundation of a complete human being. Without it, we risk becoming either heartless calculators or passionate but reckless actors. The highest expressions of humanity justice, creativity, love, and wisdom arise only when reason and feeling work together as equal partners. QUOTE 2: The unity of humanity is not a dream but a necessity: it is the only path to universal security. : The author asserts that the unity of humanity is not an idealistic dream but a fundamental necessity. In an interconnected world facing global threats climate change, pandemics, nuclear risks, resource scarcity, and technological disruption fragmented efforts and national rivalries are no longer sustainable. True universal security cannot be achieved through dominance, isolation, or temporary alliances. It requires a higher level of human solidarity: shared institutions, mutual trust, collective responsibility, and a common commitment to the survival and flourishing of our species. Without unity, every nation remains vulnerable, no matter how powerful. Unity does not mean erasing diversity or sovereignty. It means building a framework in which differences are respected while common survival imperatives are placed above them. It is the recognition that in the 21st century and beyond, humanity’s fate is collective. The path to lasting security runs through unity. Anything less is merely managed risk.

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Notice how the Alhambra's external facades are plain and simple, while the inside is most dazzling in splendour and beauty. This is a feature of the Islamic ethos. It draws from the same notions of modesty that emphasize beauty of character and public humility. The ethos that would translates into the veil, or the Sufi's simple external appearance - while he carries a glimmering ocean within. An ethos also conveyed by St Peter when he wrote: "When adorning yourselves, let it not be that outward adorning of plaiting the hair, and of wearing gold, or of putting on apparel; but let it be the hidden man of the heart which is not corruptible, even the ornament of a meek and quiet spirit, which in the sight of God is of great price."
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Notice how the Alhambra's external facades are plain and simple, while the inside is most dazzling in splendour and beauty. This is a feature of the Islamic ethos. It draws from the same notions of modesty that emphasize beauty of character and public humility. The ethos that would translates into the veil, or the Sufi's simple external appearance - while he carries a glimmering ocean within. An ethos also conveyed by St Peter when he wrote: "When adorning yourselves, let it not be that outward adorning of plaiting the hair, and of wearing gold, or of putting on apparel; but let it be the hidden man of the heart which is not corruptible, even the ornament of a meek and quiet spirit, which in the sight of God is of great price."

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Do you know why the Sphinx, the Lamassu, or the Cherubim are guardians of temples and, in ancient legends, always ask riddles that only a wise man can answer correctly? You can only pass through them if your soul is worthy. They are not demons; they are a test of your soul!

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CNN Legal Analyst Elie Honig: "Pam Bondi is, without a question, qualified to be Attorney General. She's been a prosecutor for 20 years in Florida. For 8 of those, she was the Attorney General of the state. That's a very big, very complicated job‚ and that level of experience is on par with, or better than most United States Attorneys General that we've seen over the past 50 years or so."
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CNN Legal Analyst Elie Honig: "Pam Bondi is, without a question, qualified to be Attorney General. She's been a prosecutor for 20 years in Florida. For 8 of those, she was the Attorney General of the state. That's a very big, very complicated job‚ and that level of experience is on par with, or better than most United States Attorneys General that we've seen over the past 50 years or so."

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I think a big mistake is believing that if something is here, we should be able to see it. Right? The lights in the sky and the pilots or the gods or whatever they are? I think we assume out of arrogance and ego. An insect can crawl across your hand and never understand that you are a whole entire being. It only experiences pressure, heat, vibration, and movement. A fingertip appears. A shadow passes. The insect never sees the body attached to it. The insect does not have access to the full image. Ever. I think our situation may be exactly the same. Whatever people call the phenomenon, nonhuman intelligence, gods, or something else entirely, may be present in full while we only register a portion of it. We notice effects, not the actual being. Changes in perception. Anomalies. We expect a face when all we are capable of sensing is the fingertip. Let me explain. Reports are always partial and strange. Lights, shapes, impressions, symbols, missing time, pressure, fear, calm. None of it ever shows us a full being, or the real craft; because our senses are not built to assemble it. Just like the ant cannot assemble a human from a few sensations. Now that doesn't mean what we are seeing is fake. It means the insect’s world is smaller than the thing interacting with it. I get sick of people saying there is no there there, I think they are making the same mistake the insect would make. Our reality is likely a thin slice of what actually exists. We move through a world full of forces and intelligences that exceed our resolution. We are not seeing nothing. We are seeing effects. And effects are often the only honest proof a limited observer ever gets.
0:10

I think a big mistake is believing that if something is here, we should be able to see it. Right? The lights in the sky and the pilots or the gods or whatever they are? I think we assume out of arrogance and ego. An insect can crawl across your hand and never understand that you are a whole entire being. It only experiences pressure, heat, vibration, and movement. A fingertip appears. A shadow passes. The insect never sees the body attached to it. The insect does not have access to the full image. Ever. I think our situation may be exactly the same. Whatever people call the phenomenon, nonhuman intelligence, gods, or something else entirely, may be present in full while we only register a portion of it. We notice effects, not the actual being. Changes in perception. Anomalies. We expect a face when all we are capable of sensing is the fingertip. Let me explain. Reports are always partial and strange. Lights, shapes, impressions, symbols, missing time, pressure, fear, calm. None of it ever shows us a full being, or the real craft; because our senses are not built to assemble it. Just like the ant cannot assemble a human from a few sensations. Now that doesn't mean what we are seeing is fake. It means the insect’s world is smaller than the thing interacting with it. I get sick of people saying there is no there there, I think they are making the same mistake the insect would make. Our reality is likely a thin slice of what actually exists. We move through a world full of forces and intelligences that exceed our resolution. We are not seeing nothing. We are seeing effects. And effects are often the only honest proof a limited observer ever gets.

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This is not a common man, but a leader of Owaisi's party, AIMIM. Look at his mentality I am saying again, the Muslims of my country are traitors. Whether they are a child or an adult, educated or uneducated, everyone's mentality is the same.
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This is not a common man, but a leader of Owaisi's party, AIMIM. Look at his mentality I am saying again, the Muslims of my country are traitors. Whether they are a child or an adult, educated or uneducated, everyone's mentality is the same.

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