Fitowar 30 Oktoba, 2026

Launi huɗu sun isa ga kowace taswira, ta yadda maƙwabta koyaushe suke da launi daban. An tabbatar da hakan a 1976. Amma ta yaya za a samo launukan a zahiri?

Kayan aikin gargajiya shi ne sarƙar Kempe (Kempe chain). Zaɓi launi biyu. Ka ɗauki dukan dunƙulen ƙasashe masu haɗe da juna, masu waɗannan launuka biyu kawai. Musanya su a duk faɗin dunƙulen: taswirar tana nan da launuka daidai.

Matsalar: musanya ɗaya zai iya yaɗuwa a faɗin taswirar gaba ɗaya. Tarihin baya yana buƙatar ƙarin musanya yayin da taswirori suka girma. Kowanne yana biyan cikakken zagaye kan taswirar.

Masana lissafi shida, daga Tokyo zuwa Copenhagen, sun kawar da wannan ƙarin tsada. Algorithm ɗinsu yana yi wa ƙasashe n launi cikin lokacin da ya yi daidai da n. Ana warware ƙananan sassan taswirar sau ɗaya, a ajiye su a cikin teburori, sannan a duba su kawai. Marubutan suna kiran wannan sauri mafi kyau da zai yiwu.

Tushe: Four-Coloring Planar Graphs in Linear Time, https://arxiv.org/abs/2610.39753

Lokacin da tauraro ya zama farin dwarf (white dwarf), wasu daga cikin duniyoyinsa suna tsira. Tarkacensu da suka farfashe za su iya kewaya ragowar tauraron a matsayin ƙura da gas. Masana falaki sun san irin waɗannan fayafayen gas guda 21.

Dukansu 21 suna sa hannu a haskensu iri ɗaya: ƙololuwa biyu a kowane layi. Ƙololuwa ɗaya ga gas da ke zuwa gare mu, ɗaya ga gas da ke nisanta. A kewayen WD J1328−1450, kowane layin calcium yana nuna huɗu.

Ƙololuwa huɗu suna nufin zobban gas biyu, da gibi fanko tsakaninsu. Zoben ciki yana juyawa da sauri, kamar yadda dokar Kepler ta buƙata. Kuma magnesium yana haskakawa a zoben ciki kaɗai.

Me ke raba zobba biyu, kowanne yana samar da gas ɗinsa? Marubutan suna ba da shawarar jiki mai ƙarfi ɗaya da ya tsira a cikin kowane zobe. Na cikin zai kai girman asteroid a mafi yawa. Na waje zai iya kai girman Pluto.

Tushe: A double debris disc around a white dwarf sculpted by two planetary bodies, https://arxiv.org/abs/2610.37773

"Shin zan je dakin motsa jiki sau uku a wannan makon?" A Manifold, shafin hasashe da ke amfani da kuɗin wasa, baƙi suna yin caca kan irin waɗannan tambayoyi. Nazarce-nazarcen dakin gwaji sun ce 'yan kallo suna auna shirye-shiryenmu da sanyin rai fiye da mu.

Masu bincike uku sun yi nazarin irin waɗannan kasuwanni 6,150 kan burin mutane na kansu. Farashi ya ba EH damar 49.4% a matsakaici; ya faru kashi 45.0% na lokuta. Caca kan al'amuran waje sun kusan zama daidai.

Wannan kyakkyawan fata da ya wuce kima ba ya nan lokacin da aka buɗe kasuwannin. Ya bayyana cikin kwana ɗaya na ciniki, ko da mutumin bai taɓa yin caca ba. 'Yan kallo sun saukar da al'amura zuwa damarsu ta yau da kullum, amma ba burin mutum ba.

Gyaran ya zo a makare, kuma da yawa daga cikinsa daga mutumin da kansa. Cacarsa ta kansa ta samar da kashi 38% na motsin farashi zuwa ga gaskiya. Gyaran da aka koya daga kasuwannin baya yana inganta hasashen gaba da kashi 1.5% kawai.

Tushe: Crowds Believe in You: Online Prediction Markets Overestimate How Often People Achieve Their Own Goals, https://arxiv.org/abs/2610.40324

Haɗa ƙwayoyi masu tauri cikin abu mai laushi, sai ya ƙara tauri. Amma ka'ida ta sanya iyaka. Ƙwayoyin da suka cike kashi ɗaya cikin goma na girman abu suna ƙara 25% a mafi yawa.

Wata ƙungiyar Amurka da Jamus ta gwada digon ruwa na DNA a maimakon haka. Sun shuka su cikin cuɗanyar actin, zaren da aka ciro daga tsoka. Digon sun cike ƙasa da kashi ɗaya cikin goma na girman.

Da aka sanyaya shi zuwa 10 °C, haɗin ya yi tauri ninki 25. Ba ƙarin tauri na 25% ba: ninki 25! Ka ɗumama shi sama da 31 °C, digon su narke, sai ya sake yin laushi. Sauyin yana ɗaukar kusan minti goma, kuma yana aiki sau da sau.

Ta yaya digo ke wuce iyakar? Zare suna ratsawa kai tsaye ta cikin kowane digo kuma ana riƙe su a ciki. Idan aka murɗa abin, kowane digo yana juyawa yana jan zarensa tare da shi. Isarsa ta ninku, kuma digon suna haɗuwa su zama raga ɗaya mai ƙarfi.

Tushe: Extraordinary stiffening and reciprocal control in a DNA condensate/actin composite, https://arxiv.org/abs/2610.38504

Ɗauki wata hanyar sadarwa (network) inda kowane ɗigo biyu ke da nisan mahaɗi biyu a mafi yawa. Ƙara doka: yanke kowane mahaɗi ɗaya dole ya karya wannan. Mahaɗi nawa irin wannan hanyar sadarwa za ta iya ɗauka?

Hasashen Murty–Simon ya sanya iyakar: adadin ɗigo murabba'i, raba da huɗu. Ɗigo goma, mahaɗi 25 a mafi yawa. Hanyar sadarwa ɗaya kawai ke kaiwa gare ta. Rukuni biyu masu daidaito gwargwadon yiwuwa, kowane ɗigo an haɗa shi da kowane ɗigo na ɗayan rukunin.

A 1992, Zoltán Füredi ya tabbatar da shi, amma ga manyan hanyoyin sadarwa ƙwarai kawai. Suna buƙatar ɗigo fiye da hasumiyar 2 mai tsawon kusan hawa 10¹⁴. Kowane hawa yana ɗaga 2 zuwa ƙarfin duk abin da ke samansa.

Sanjana Das da Jacob Fox, a Stanford, yanzu sun tabbatar da shi ga kowane girma. Wani AI, GPT-5.6 Sol, ne ya samo yawancin hujjar. Hujjarsu ta kansu ta nuna cewa hanyar sadarwa ta rukuni biyu kaɗai ke kaiwa iyakar.

Tushe: A proof of the Murty–Simon conjecture on diameter-2-critical graphs, https://arxiv.org/abs/2610.39032

Proton biyu, electron biyu: ƙwayar hydrogen ita ce mafi sauƙi da ake da ita. Makamashi nawa ke raba ta biyu? A 1913, ƙiyasin Bohr ya gaza da kusan kashi 40%.

Masana kimiyyar lissafi suna auna irin waɗannan makamashi a matsayin mitocin haske, da hertz. Wata ƙungiya daga ETH Zurich da VU Amsterdam ta hau tsanin makamashin ƙwayar. Laser da igiyoyin millimetre ne suka yi hawan, mataki-mataki.

Yanzu an san makamashin da ke raba H₂ cikin kilohertz 175. Wannan kusan kashi 1.6 ne cikin biliyan goma. Daidaiton mafi kyawun lissafi ya gaza na wannan fiye da ninki biyar.

Hydrogen yana zuwa a sigogi biyu, waɗanda proton ɗinsu ke juyawa daban. Gibin makamashi tsakaninsu ya yi daidai da ka'ida. Duk wani ilimin kimiyyar lissafi da ba a sani ba da ke bambanta su yana ƙasa da kilohertz 540. Yanzu ka'idar tana buƙatar a lissafa gyaranta na α⁷ gaba ɗaya.

Tushe: Ionization and Dissociation Energies of Molecular Hydrogen, https://arxiv.org/abs/2610.40359

A 2009, masana ka'ida sun yi hasashen cewa hasken da filinsa ke juyawa a da'ira zai iya sauya graphene. Graphene za ta zama topological insulator, wadda siffar igiyoyin electron ɗinta ke ayyana ta.

Gwada hakan yana da wuya. Electron a cikin graphene suna karo da juna da sauri ƙwarai, wanda zai iya dushe tasirin. Gwaje-gwajen baya da suka ɗauki hoton maɗauranta sun yi amfani da hasken da ke kai-komo. Irin wannan haske ba zai iya samar da wannan yanayi ba.

Wata ƙungiya da Bordeaux ke jagoranta ta harbi graphene da bugun hasken infrared masu tsawon femtosecond 135. Femtosecond kashi ɗaya ne cikin miliyan na biliyan ɗaya na daƙiƙa. A lokacin kowane bugu, walƙiyoyin extreme-ultraviolet sun fitar da electron don karanta yanayinsu.

Kusa da wurin da maɗaurin makamashin graphene ke haɗuwa, wata sabuwar alama ta bayyana. Alamarta (sign) ta juye a duk lokacin da hasken ya juya ta ɗayan hanya. Gibin da ake tsammani a makamashin electron bai bayyana ba; juyewar ita ce shaidarsu.

Tushe: Observation of light-induced topological state in graphene, https://arxiv.org/abs/2610.39695

Exciton electron ne da aka ɗaure da rami (hole), wato wurin da electron ya ɓace. Nau'in ba ya ɗauke da cajin lantarki. Idan an sanyaya su sosai, exciton za su iya samar da superfluid, ruwa da ke motsi a matsayin igiyar kwantum ɗaya.

Wannan rashin caji yana sa superfluid ɗinsu wahalar gani. Wata ƙungiyar Princeton ta ɗora zanen gado biyu na graphene da tazarar nanometre 3.2, a cikin filin maganaɗisu mai ƙarfi. Electron a cikin zanen gado ɗaya sun haɗu da ramuka a ɗayan.

Sannan ƙungiyar ta ƙara ɗan ƙarin caji. Ka'ida ta ce zai zauna a cikin ƙananan guguwa, a kulle cikin tsari. Na'urar hangen nesa ta tunnelling ta sami tsarin caji wanda tazararsa ta yi daidai da ka'idar.

Motsa caji daga zanen gado ɗaya zuwa ɗayan bai canza wannan tazarar ba. Lu'ulu'un electron a zanen gado na sama zai canza ta. Wannan yana nuni ga nau'i-nau'i da ke raba ƙari ɗaya na kwantum.

Tushe: Evidence for a charged vortex lattice in an exciton superfluid, https://arxiv.org/abs/2610.37781

A ranar 11 ga Yuli 1991, wani tashar kallon sararin samaniya ya kama walƙiyar hasken gamma. Kololuwarta mai haske ta ɗauki kusan millisecond goma. Tushenta? Taurari biyu masu matsewa da ke haɗuwa, ko magnetar.

Magnetar tauraron neutron ne mai filin maganaɗisu mai ƙarfin gaske. A 2020, wani ya saki babbar fashewa a wani galaxy na kusa. Wata ƙungiya daga China da Amurka ta kwatanta walƙiyoyin biyu.

Siffa ɗaya: kololuwa mai kaifi, sannan wutsiya mai rauni. Ƙari ɗaya ma. Dukansu suna haskakawa suna dushewa a cikakkun ninkin kusan sau 360 a kowane daƙiƙa. Waɗannan bugun suna kama da haɗaɗɗu, kamar ƙarin sautukan (overtones) wata nota ɗaya.

A wajen marubutan, fashewar magnetar tana bayyana shi cikin sauƙi fiye da haɗuwar taurari. Ba su kai ga cewa an tabbatar ba. Galaxy goma sha bakwai na kusa suna iya zama masaukinta.

Tushe: Harmonic brightness oscillations point to magnetar giant flares in rare short gamma-ray bursts, https://arxiv.org/abs/2610.39130

Ɗan caca shida, zagaye ɗaya. Na farko yana doke na biyu, na biyu yana doke na uku, haka dai. Sannan na shida yana doke na farko. Babu ɗan caca da ya fi duka.

Dokokin suna da tsauri. Fuskoki shida, kowacce tana nuna ƙima daga 1 zuwa 6, ana yarda da maimaitawa. Kowace nasara tana zuwa da mafi ƙanƙantar tazara da za ta yiwu: gwabzawa 19 cikin 36.

Terry Easlick, a Université de Montréal, ya sa kwamfuta ta tsara dukan irin waɗannan 'yan caca 462. Da fuskoki uku, huɗu ko biyar, babu zagaye da ke samuwa a mafi ƙanƙantar tazararsu. Da fuskoki shida, zagaye biyu daidai ne ke akwai.

Zagaye biyun hoton madubi ne na juna. Mayar da kowace fuska v zuwa 7 − v, juya kibiyoyin: za ka sami ɗayan. Da fuskoki bakwai zuwa goma, zagaye suna tsawaita fiye da adadin fuskoki. Shin shida ne kaɗai lambar da ta dace? Har yanzu hasashe ne.

Tushe: Computer-Assisted Results for n-Sided Non-Transitive Dice Taking Face Values in [n], https://arxiv.org/abs/2610.40321

Bayan manyan karo, mai yiwuwa tekun narkakken dutse ya rufe Duniya a ƙuruciyarta. A samansa akwai yanayi (atmosphere) mai kauri, galibi hydrogen. Can ƙasa a zurfi, matsi mai murƙushewa ya raba ƙarfe zuwa ƙarfe na ƙarfe (metal) da ƙarfen da aka haɗa da oxygen. Ƙarfen ƙarfe ya nutse zuwa tsakiyar duniya.

Hydrogen da ƙarfen da aka haɗa da oxygen suna samar da ruwa. Amma hydrogen yana shiga cikin narkakken dutse ne a hankali kawai. To shin wannan ilimin sinadarai zai iya yin tasiri? Wata ƙungiya a Japan ta gina samfurin lissafi don ta gano.

Amsar tana cikin fatar magma. Idan aka sanyaya ta daga sama, tana nutsewa kusan kowane minti ɗaya. Sabon narkakken dutse yana maye gurbinta kuma yana ci gaba da shan hydrogen. Yawancin hydrogen ɗin yana zama ruwa cikin kusan shekaru 10,000.

Zurfin tekun magma, yawan ruwan da yake samarwa. Idan akwai isasshen hydrogen, wannan zai iya bayyana adadin ruwan Duniya, marubutan sun rubuta. Kuma sararin zai ci gaba da kasancewa cike da hydrogen.

Tushe: Coupled evolution of Earth's H2-rich proto-atmosphere and oxidized magma ocean: Efficient H2O production through dissolved H2 transport and atmospheric buffering of the magma ocean redox state, https://arxiv.org/abs/2610.38503